Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [70,3,Mod(43,70)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(70, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("70.43");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 70 = 2 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 70.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.90736185052\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{14})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 49 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 57.2 | ||
Root | \(1.87083 - 1.87083i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 70.57 |
Dual form | 70.3.f.a.43.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/70\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(57\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.00000i | −0.500000 | − | 0.500000i | ||||
\(3\) | 2.87083 | − | 2.87083i | 0.956943 | − | 0.956943i | −0.0421677 | − | 0.999111i | \(-0.513426\pi\) |
0.999111 | + | 0.0421677i | \(0.0134264\pi\) | |||||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | 4.87083 | + | 1.12917i | 0.974166 | + | 0.225834i | ||||
\(6\) | −5.74166 | −0.956943 | ||||||||
\(7\) | −1.87083 | − | 1.87083i | −0.267261 | − | 0.267261i | ||||
\(8\) | 2.00000 | − | 2.00000i | 0.250000 | − | 0.250000i | ||||
\(9\) | − | 7.48331i | − | 0.831479i | ||||||
\(10\) | −3.74166 | − | 6.00000i | −0.374166 | − | 0.600000i | ||||
\(11\) | −13.9666 | −1.26969 | −0.634847 | − | 0.772638i | \(-0.718937\pi\) | ||||
−0.634847 | + | 0.772638i | \(0.718937\pi\) | |||||||
\(12\) | 5.74166 | + | 5.74166i | 0.478471 | + | 0.478471i | ||||
\(13\) | 6.61249 | − | 6.61249i | 0.508653 | − | 0.508653i | −0.405460 | − | 0.914113i | \(-0.632889\pi\) |
0.914113 | + | 0.405460i | \(0.132889\pi\) | |||||||
\(14\) | 3.74166i | 0.267261i | ||||||||
\(15\) | 17.2250 | − | 10.7417i | 1.14833 | − | 0.716110i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | 8.09580 | + | 8.09580i | 0.476224 | + | 0.476224i | 0.903922 | − | 0.427698i | \(-0.140675\pi\) |
−0.427698 | + | 0.903922i | \(0.640675\pi\) | |||||||
\(18\) | −7.48331 | + | 7.48331i | −0.415740 | + | 0.415740i | ||||
\(19\) | 14.2583i | 0.750439i | 0.926936 | + | 0.375220i | \(0.122433\pi\) | ||||
−0.926936 | + | 0.375220i | \(0.877567\pi\) | |||||||
\(20\) | −2.25834 | + | 9.74166i | −0.112917 | + | 0.487083i | ||||
\(21\) | −10.7417 | −0.511507 | ||||||||
\(22\) | 13.9666 | + | 13.9666i | 0.634847 | + | 0.634847i | ||||
\(23\) | −28.7083 | + | 28.7083i | −1.24819 | + | 1.24819i | −0.291666 | + | 0.956520i | \(0.594210\pi\) |
−0.956520 | + | 0.291666i | \(0.905790\pi\) | |||||||
\(24\) | − | 11.4833i | − | 0.478471i | ||||||
\(25\) | 22.4499 | + | 11.0000i | 0.897998 | + | 0.440000i | ||||
\(26\) | −13.2250 | −0.508653 | ||||||||
\(27\) | 4.35414 | + | 4.35414i | 0.161265 | + | 0.161265i | ||||
\(28\) | 3.74166 | − | 3.74166i | 0.133631 | − | 0.133631i | ||||
\(29\) | − | 20.0334i | − | 0.690806i | −0.938454 | − | 0.345403i | \(-0.887742\pi\) | ||
0.938454 | − | 0.345403i | \(-0.112258\pi\) | |||||||
\(30\) | −27.9666 | − | 6.48331i | −0.932221 | − | 0.216110i | ||||
\(31\) | 0.775028 | 0.0250009 | 0.0125004 | − | 0.999922i | \(-0.496021\pi\) | ||||
0.0125004 | + | 0.999922i | \(0.496021\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.125000 | + | 0.125000i | ||||
\(33\) | −40.0958 | + | 40.0958i | −1.21502 | + | 1.21502i | ||||
\(34\) | − | 16.1916i | − | 0.476224i | ||||||
\(35\) | −7.00000 | − | 11.2250i | −0.200000 | − | 0.320713i | ||||
\(36\) | 14.9666 | 0.415740 | ||||||||
\(37\) | 37.2250 | + | 37.2250i | 1.00608 | + | 1.00608i | 0.999981 | + | 0.00609893i | \(0.00194136\pi\) |
0.00609893 | + | 0.999981i | \(0.498059\pi\) | |||||||
\(38\) | 14.2583 | − | 14.2583i | 0.375220 | − | 0.375220i | ||||
\(39\) | − | 37.9666i | − | 0.973503i | ||||||
\(40\) | 12.0000 | − | 7.48331i | 0.300000 | − | 0.187083i | ||||
\(41\) | −29.6749 | −0.723778 | −0.361889 | − | 0.932221i | \(-0.617868\pi\) | ||||
−0.361889 | + | 0.932221i | \(0.617868\pi\) | |||||||
\(42\) | 10.7417 | + | 10.7417i | 0.255754 | + | 0.255754i | ||||
\(43\) | 54.4833 | − | 54.4833i | 1.26705 | − | 1.26705i | 0.319451 | − | 0.947603i | \(-0.396501\pi\) |
0.947603 | − | 0.319451i | \(-0.103499\pi\) | |||||||
\(44\) | − | 27.9333i | − | 0.634847i | ||||||
\(45\) | 8.44994 | − | 36.4499i | 0.187777 | − | 0.809999i | ||||
\(46\) | 57.4166 | 1.24819 | ||||||||
\(47\) | −64.0291 | − | 64.0291i | −1.36232 | − | 1.36232i | −0.870952 | − | 0.491369i | \(-0.836497\pi\) |
−0.491369 | − | 0.870952i | \(-0.663503\pi\) | |||||||
\(48\) | −11.4833 | + | 11.4833i | −0.239236 | + | 0.239236i | ||||
\(49\) | 7.00000i | 0.142857i | ||||||||
\(50\) | −11.4499 | − | 33.4499i | −0.228999 | − | 0.668999i | ||||
\(51\) | 46.4833 | 0.911438 | ||||||||
\(52\) | 13.2250 | + | 13.2250i | 0.254326 | + | 0.254326i | ||||
\(53\) | −17.7083 | + | 17.7083i | −0.334119 | + | 0.334119i | −0.854148 | − | 0.520030i | \(-0.825921\pi\) |
0.520030 | + | 0.854148i | \(0.325921\pi\) | |||||||
\(54\) | − | 8.70829i | − | 0.161265i | ||||||
\(55\) | −68.0291 | − | 15.7707i | −1.23689 | − | 0.286740i | ||||
\(56\) | −7.48331 | −0.133631 | ||||||||
\(57\) | 40.9333 | + | 40.9333i | 0.718127 | + | 0.718127i | ||||
\(58\) | −20.0334 | + | 20.0334i | −0.345403 | + | 0.345403i | ||||
\(59\) | 60.1249i | 1.01907i | 0.860451 | + | 0.509533i | \(0.170182\pi\) | ||||
−0.860451 | + | 0.509533i | \(0.829818\pi\) | |||||||
\(60\) | 21.4833 | + | 34.4499i | 0.358055 | + | 0.574166i | ||||
\(61\) | −86.9666 | −1.42568 | −0.712841 | − | 0.701325i | \(-0.752592\pi\) | ||||
−0.712841 | + | 0.701325i | \(0.752592\pi\) | |||||||
\(62\) | −0.775028 | − | 0.775028i | −0.0125004 | − | 0.0125004i | ||||
\(63\) | −14.0000 | + | 14.0000i | −0.222222 | + | 0.222222i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 39.6749 | − | 24.7417i | 0.610383 | − | 0.380641i | ||||
\(66\) | 80.1916 | 1.21502 | ||||||||
\(67\) | −41.7083 | − | 41.7083i | −0.622512 | − | 0.622512i | 0.323661 | − | 0.946173i | \(-0.395086\pi\) |
−0.946173 | + | 0.323661i | \(0.895086\pi\) | |||||||
\(68\) | −16.1916 | + | 16.1916i | −0.238112 | + | 0.238112i | ||||
\(69\) | 164.833i | 2.38889i | ||||||||
\(70\) | −4.22497 | + | 18.2250i | −0.0603567 | + | 0.260357i | ||||
\(71\) | −47.4833 | −0.668779 | −0.334390 | − | 0.942435i | \(-0.608530\pi\) | ||||
−0.334390 | + | 0.942435i | \(0.608530\pi\) | |||||||
\(72\) | −14.9666 | − | 14.9666i | −0.207870 | − | 0.207870i | ||||
\(73\) | 34.3832 | − | 34.3832i | 0.471003 | − | 0.471003i | −0.431236 | − | 0.902239i | \(-0.641922\pi\) |
0.902239 | + | 0.431236i | \(0.141922\pi\) | |||||||
\(74\) | − | 74.4499i | − | 1.00608i | ||||||
\(75\) | 96.0291 | − | 32.8708i | 1.28039 | − | 0.438278i | ||||
\(76\) | −28.5167 | −0.375220 | ||||||||
\(77\) | 26.1292 | + | 26.1292i | 0.339340 | + | 0.339340i | ||||
\(78\) | −37.9666 | + | 37.9666i | −0.486752 | + | 0.486752i | ||||
\(79\) | − | 9.13348i | − | 0.115614i | −0.998328 | − | 0.0578068i | \(-0.981589\pi\) | ||
0.998328 | − | 0.0578068i | \(-0.0184108\pi\) | |||||||
\(80\) | −19.4833 | − | 4.51669i | −0.243541 | − | 0.0564586i | ||||
\(81\) | 92.3498 | 1.14012 | ||||||||
\(82\) | 29.6749 | + | 29.6749i | 0.361889 | + | 0.361889i | ||||
\(83\) | 78.9666 | − | 78.9666i | 0.951405 | − | 0.951405i | −0.0474676 | − | 0.998873i | \(-0.515115\pi\) |
0.998873 | + | 0.0474676i | \(0.0151151\pi\) | |||||||
\(84\) | − | 21.4833i | − | 0.255754i | ||||||
\(85\) | 30.2917 | + | 48.5748i | 0.356373 | + | 0.571468i | ||||
\(86\) | −108.967 | −1.26705 | ||||||||
\(87\) | −57.5124 | − | 57.5124i | −0.661062 | − | 0.661062i | ||||
\(88\) | −27.9333 | + | 27.9333i | −0.317423 | + | 0.317423i | ||||
\(89\) | 80.0000i | 0.898876i | 0.893311 | + | 0.449438i | \(0.148376\pi\) | ||||
−0.893311 | + | 0.449438i | \(0.851624\pi\) | |||||||
\(90\) | −44.8999 | + | 28.0000i | −0.498888 | + | 0.311111i | ||||
\(91\) | −24.7417 | −0.271886 | ||||||||
\(92\) | −57.4166 | − | 57.4166i | −0.624093 | − | 0.624093i | ||||
\(93\) | 2.22497 | − | 2.22497i | 0.0239244 | − | 0.0239244i | ||||
\(94\) | 128.058i | 1.36232i | ||||||||
\(95\) | −16.1001 | + | 69.4499i | −0.169475 | + | 0.731052i | ||||
\(96\) | 22.9666 | 0.239236 | ||||||||
\(97\) | −56.5457 | − | 56.5457i | −0.582946 | − | 0.582946i | 0.352766 | − | 0.935712i | \(-0.385241\pi\) |
−0.935712 | + | 0.352766i | \(0.885241\pi\) | |||||||
\(98\) | 7.00000 | − | 7.00000i | 0.0714286 | − | 0.0714286i | ||||
\(99\) | 104.517i | 1.05572i | ||||||||
\(100\) | −22.0000 | + | 44.8999i | −0.220000 | + | 0.448999i | ||||
\(101\) | −76.5748 | −0.758166 | −0.379083 | − | 0.925363i | \(-0.623761\pi\) | ||||
−0.379083 | + | 0.925363i | \(0.623761\pi\) | |||||||
\(102\) | −46.4833 | − | 46.4833i | −0.455719 | − | 0.455719i | ||||
\(103\) | 56.5457 | − | 56.5457i | 0.548988 | − | 0.548988i | −0.377160 | − | 0.926148i | \(-0.623099\pi\) |
0.926148 | + | 0.377160i | \(0.123099\pi\) | |||||||
\(104\) | − | 26.4499i | − | 0.254326i | ||||||
\(105\) | −52.3208 | − | 12.1292i | −0.498293 | − | 0.115516i | ||||
\(106\) | 35.4166 | 0.334119 | ||||||||
\(107\) | −27.3832 | − | 27.3832i | −0.255918 | − | 0.255918i | 0.567474 | − | 0.823392i | \(-0.307921\pi\) |
−0.823392 | + | 0.567474i | \(0.807921\pi\) | |||||||
\(108\) | −8.70829 | + | 8.70829i | −0.0806323 | + | 0.0806323i | ||||
\(109\) | − | 154.867i | − | 1.42079i | −0.703801 | − | 0.710397i | \(-0.748515\pi\) | ||
0.703801 | − | 0.710397i | \(-0.251485\pi\) | |||||||
\(110\) | 52.2583 | + | 83.7998i | 0.475076 | + | 0.761816i | ||||
\(111\) | 213.733 | 1.92552 | ||||||||
\(112\) | 7.48331 | + | 7.48331i | 0.0668153 | + | 0.0668153i | ||||
\(113\) | 99.0247 | − | 99.0247i | 0.876325 | − | 0.876325i | −0.116827 | − | 0.993152i | \(-0.537272\pi\) |
0.993152 | + | 0.116827i | \(0.0372723\pi\) | |||||||
\(114\) | − | 81.8665i | − | 0.718127i | ||||||
\(115\) | −172.250 | + | 107.417i | −1.49782 | + | 0.934057i | ||||
\(116\) | 40.0667 | 0.345403 | ||||||||
\(117\) | −49.4833 | − | 49.4833i | −0.422934 | − | 0.422934i | ||||
\(118\) | 60.1249 | − | 60.1249i | 0.509533 | − | 0.509533i | ||||
\(119\) | − | 30.2917i | − | 0.254552i | ||||||
\(120\) | 12.9666 | − | 55.9333i | 0.108055 | − | 0.466110i | ||||
\(121\) | 74.0667 | 0.612122 | ||||||||
\(122\) | 86.9666 | + | 86.9666i | 0.712841 | + | 0.712841i | ||||
\(123\) | −85.1916 | + | 85.1916i | −0.692615 | + | 0.692615i | ||||
\(124\) | 1.55006i | 0.0125004i | ||||||||
\(125\) | 96.9289 | + | 78.9289i | 0.775432 | + | 0.631432i | ||||
\(126\) | 28.0000 | 0.222222 | ||||||||
\(127\) | 64.2917 | + | 64.2917i | 0.506234 | + | 0.506234i | 0.913368 | − | 0.407134i | \(-0.133472\pi\) |
−0.407134 | + | 0.913368i | \(0.633472\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | − | 312.825i | − | 2.42500i | ||||||
\(130\) | −64.4166 | − | 14.9333i | −0.495512 | − | 0.114871i | ||||
\(131\) | 146.633 | 1.11934 | 0.559668 | − | 0.828717i | \(-0.310929\pi\) | ||||
0.559668 | + | 0.828717i | \(0.310929\pi\) | |||||||
\(132\) | −80.1916 | − | 80.1916i | −0.607512 | − | 0.607512i | ||||
\(133\) | 26.6749 | − | 26.6749i | 0.200563 | − | 0.200563i | ||||
\(134\) | 83.4166i | 0.622512i | ||||||||
\(135\) | 16.2917 | + | 26.1249i | 0.120679 | + | 0.193517i | ||||
\(136\) | 32.3832 | 0.238112 | ||||||||
\(137\) | −7.34983 | − | 7.34983i | −0.0536484 | − | 0.0536484i | 0.679774 | − | 0.733422i | \(-0.262078\pi\) |
−0.733422 | + | 0.679774i | \(0.762078\pi\) | |||||||
\(138\) | 164.833 | − | 164.833i | 1.19444 | − | 1.19444i | ||||
\(139\) | 53.8665i | 0.387529i | 0.981048 | + | 0.193764i | \(0.0620698\pi\) | ||||
−0.981048 | + | 0.193764i | \(0.937930\pi\) | |||||||
\(140\) | 22.4499 | − | 14.0000i | 0.160357 | − | 0.100000i | ||||
\(141\) | −367.633 | −2.60733 | ||||||||
\(142\) | 47.4833 | + | 47.4833i | 0.334390 | + | 0.334390i | ||||
\(143\) | −92.3541 | + | 92.3541i | −0.645833 | + | 0.645833i | ||||
\(144\) | 29.9333i | 0.207870i | ||||||||
\(145\) | 22.6211 | − | 97.5791i | 0.156008 | − | 0.672959i | ||||
\(146\) | −68.7664 | −0.471003 | ||||||||
\(147\) | 20.0958 | + | 20.0958i | 0.136706 | + | 0.136706i | ||||
\(148\) | −74.4499 | + | 74.4499i | −0.503040 | + | 0.503040i | ||||
\(149\) | − | 84.6502i | − | 0.568122i | −0.958806 | − | 0.284061i | \(-0.908318\pi\) | ||
0.958806 | − | 0.284061i | \(-0.0916818\pi\) | |||||||
\(150\) | −128.900 | − | 63.1582i | −0.859333 | − | 0.421055i | ||||
\(151\) | −21.8331 | −0.144590 | −0.0722952 | − | 0.997383i | \(-0.523032\pi\) | ||||
−0.0722952 | + | 0.997383i | \(0.523032\pi\) | |||||||
\(152\) | 28.5167 | + | 28.5167i | 0.187610 | + | 0.187610i | ||||
\(153\) | 60.5834 | − | 60.5834i | 0.395970 | − | 0.395970i | ||||
\(154\) | − | 52.2583i | − | 0.339340i | ||||||
\(155\) | 3.77503 | + | 0.875139i | 0.0243550 | + | 0.00564606i | ||||
\(156\) | 75.9333 | 0.486752 | ||||||||
\(157\) | 34.8331 | + | 34.8331i | 0.221867 | + | 0.221867i | 0.809284 | − | 0.587417i | \(-0.199855\pi\) |
−0.587417 | + | 0.809284i | \(0.699855\pi\) | |||||||
\(158\) | −9.13348 | + | 9.13348i | −0.0578068 | + | 0.0578068i | ||||
\(159\) | 101.675i | 0.639465i | ||||||||
\(160\) | 14.9666 | + | 24.0000i | 0.0935414 | + | 0.150000i | ||||
\(161\) | 107.417 | 0.667184 | ||||||||
\(162\) | −92.3498 | − | 92.3498i | −0.570061 | − | 0.570061i | ||||
\(163\) | −45.2250 | + | 45.2250i | −0.277454 | + | 0.277454i | −0.832092 | − | 0.554638i | \(-0.812857\pi\) |
0.554638 | + | 0.832092i | \(0.312857\pi\) | |||||||
\(164\) | − | 59.3498i | − | 0.361889i | ||||||
\(165\) | −240.575 | + | 150.025i | −1.45803 | + | 0.909241i | ||||
\(166\) | −157.933 | −0.951405 | ||||||||
\(167\) | −78.0377 | − | 78.0377i | −0.467292 | − | 0.467292i | 0.433744 | − | 0.901036i | \(-0.357192\pi\) |
−0.901036 | + | 0.433744i | \(0.857192\pi\) | |||||||
\(168\) | −21.4833 | + | 21.4833i | −0.127877 | + | 0.127877i | ||||
\(169\) | 81.5501i | 0.482545i | ||||||||
\(170\) | 18.2831 | − | 78.8665i | 0.107548 | − | 0.463921i | ||||
\(171\) | 106.700 | 0.623975 | ||||||||
\(172\) | 108.967 | + | 108.967i | 0.633527 | + | 0.633527i | ||||
\(173\) | −102.087 | + | 102.087i | −0.590099 | + | 0.590099i | −0.937658 | − | 0.347559i | \(-0.887011\pi\) |
0.347559 | + | 0.937658i | \(0.387011\pi\) | |||||||
\(174\) | 115.025i | 0.661062i | ||||||||
\(175\) | −21.4209 | − | 62.5791i | −0.122405 | − | 0.357595i | ||||
\(176\) | 55.8665 | 0.317423 | ||||||||
\(177\) | 172.608 | + | 172.608i | 0.975187 | + | 0.975187i | ||||
\(178\) | 80.0000 | − | 80.0000i | 0.449438 | − | 0.449438i | ||||
\(179\) | 248.250i | 1.38687i | 0.720519 | + | 0.693435i | \(0.243904\pi\) | ||||
−0.720519 | + | 0.693435i | \(0.756096\pi\) | |||||||
\(180\) | 72.8999 | + | 16.8999i | 0.404999 | + | 0.0938883i | ||||
\(181\) | −17.1582 | −0.0947969 | −0.0473984 | − | 0.998876i | \(-0.515093\pi\) | ||||
−0.0473984 | + | 0.998876i | \(0.515093\pi\) | |||||||
\(182\) | 24.7417 | + | 24.7417i | 0.135943 | + | 0.135943i | ||||
\(183\) | −249.666 | + | 249.666i | −1.36430 | + | 1.36430i | ||||
\(184\) | 114.833i | 0.624093i | ||||||||
\(185\) | 139.283 | + | 223.350i | 0.752882 | + | 1.20730i | ||||
\(186\) | −4.44994 | −0.0239244 | ||||||||
\(187\) | −113.071 | − | 113.071i | −0.604658 | − | 0.604658i | ||||
\(188\) | 128.058 | − | 128.058i | 0.681160 | − | 0.681160i | ||||
\(189\) | − | 16.2917i | − | 0.0861995i | ||||||
\(190\) | 85.5501 | − | 53.3498i | 0.450263 | − | 0.280789i | ||||
\(191\) | 200.916 | 1.05192 | 0.525958 | − | 0.850510i | \(-0.323707\pi\) | ||||
0.525958 | + | 0.850510i | \(0.323707\pi\) | |||||||
\(192\) | −22.9666 | − | 22.9666i | −0.119618 | − | 0.119618i | ||||
\(193\) | 121.800 | − | 121.800i | 0.631087 | − | 0.631087i | −0.317254 | − | 0.948341i | \(-0.602761\pi\) |
0.948341 | + | 0.317254i | \(0.102761\pi\) | |||||||
\(194\) | 113.091i | 0.582946i | ||||||||
\(195\) | 42.8708 | − | 184.929i | 0.219850 | − | 0.948354i | ||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | −215.125 | − | 215.125i | −1.09200 | − | 1.09200i | −0.995315 | − | 0.0966898i | \(-0.969175\pi\) |
−0.0966898 | − | 0.995315i | \(-0.530825\pi\) | |||||||
\(198\) | 104.517 | − | 104.517i | 0.527862 | − | 0.527862i | ||||
\(199\) | − | 93.2917i | − | 0.468803i | −0.972140 | − | 0.234401i | \(-0.924687\pi\) | ||
0.972140 | − | 0.234401i | \(-0.0753130\pi\) | |||||||
\(200\) | 66.8999 | − | 22.8999i | 0.334499 | − | 0.114499i | ||||
\(201\) | −239.475 | −1.19142 | ||||||||
\(202\) | 76.5748 | + | 76.5748i | 0.379083 | + | 0.379083i | ||||
\(203\) | −37.4790 | + | 37.4790i | −0.184626 | + | 0.184626i | ||||
\(204\) | 92.9666i | 0.455719i | ||||||||
\(205\) | −144.541 | − | 33.5081i | −0.705080 | − | 0.163454i | ||||
\(206\) | −113.091 | −0.548988 | ||||||||
\(207\) | 214.833 | + | 214.833i | 1.03784 | + | 1.03784i | ||||
\(208\) | −26.4499 | + | 26.4499i | −0.127163 | + | 0.127163i | ||||
\(209\) | − | 199.141i | − | 0.952828i | ||||||
\(210\) | 40.1916 | + | 64.4499i | 0.191389 | + | 0.306904i | ||||
\(211\) | −74.3498 | −0.352369 | −0.176184 | − | 0.984357i | \(-0.556376\pi\) | ||||
−0.176184 | + | 0.984357i | \(0.556376\pi\) | |||||||
\(212\) | −35.4166 | − | 35.4166i | −0.167059 | − | 0.167059i | ||||
\(213\) | −136.316 | + | 136.316i | −0.639983 | + | 0.639983i | ||||
\(214\) | 54.7664i | 0.255918i | ||||||||
\(215\) | 326.900 | − | 203.858i | 1.52046 | − | 0.948176i | ||||
\(216\) | 17.4166 | 0.0806323 | ||||||||
\(217\) | −1.44994 | − | 1.44994i | −0.00668177 | − | 0.00668177i | ||||
\(218\) | −154.867 | + | 154.867i | −0.710397 | + | 0.710397i | ||||
\(219\) | − | 197.417i | − | 0.901446i | ||||||
\(220\) | 31.5414 | − | 136.058i | 0.143370 | − | 0.618446i | ||||
\(221\) | 107.067 | 0.484465 | ||||||||
\(222\) | −213.733 | − | 213.733i | −0.962761 | − | 0.962761i | ||||
\(223\) | −112.929 | + | 112.929i | −0.506408 | + | 0.506408i | −0.913422 | − | 0.407014i | \(-0.866570\pi\) |
0.407014 | + | 0.913422i | \(0.366570\pi\) | |||||||
\(224\) | − | 14.9666i | − | 0.0668153i | ||||||
\(225\) | 82.3165 | − | 168.000i | 0.365851 | − | 0.746667i | ||||
\(226\) | −198.049 | −0.876325 | ||||||||
\(227\) | 85.7793 | + | 85.7793i | 0.377883 | + | 0.377883i | 0.870338 | − | 0.492455i | \(-0.163900\pi\) |
−0.492455 | + | 0.870338i | \(0.663900\pi\) | |||||||
\(228\) | −81.8665 | + | 81.8665i | −0.359064 | + | 0.359064i | ||||
\(229\) | 215.875i | 0.942686i | 0.881950 | + | 0.471343i | \(0.156231\pi\) | ||||
−0.881950 | + | 0.471343i | \(0.843769\pi\) | |||||||
\(230\) | 279.666 | + | 64.8331i | 1.21594 | + | 0.281883i | ||||
\(231\) | 150.025 | 0.649458 | ||||||||
\(232\) | −40.0667 | − | 40.0667i | −0.172701 | − | 0.172701i | ||||
\(233\) | −77.5501 | + | 77.5501i | −0.332833 | + | 0.332833i | −0.853661 | − | 0.520828i | \(-0.825623\pi\) |
0.520828 | + | 0.853661i | \(0.325623\pi\) | |||||||
\(234\) | 98.9666i | 0.422934i | ||||||||
\(235\) | −239.575 | − | 384.174i | −1.01947 | − | 1.63478i | ||||
\(236\) | −120.250 | −0.509533 | ||||||||
\(237\) | −26.2207 | − | 26.2207i | −0.110636 | − | 0.110636i | ||||
\(238\) | −30.2917 | + | 30.2917i | −0.127276 | + | 0.127276i | ||||
\(239\) | − | 30.4661i | − | 0.127473i | −0.997967 | − | 0.0637366i | \(-0.979698\pi\) | ||
0.997967 | − | 0.0637366i | \(-0.0203017\pi\) | |||||||
\(240\) | −68.8999 | + | 42.9666i | −0.287083 | + | 0.179028i | ||||
\(241\) | 40.3337 | 0.167360 | 0.0836799 | − | 0.996493i | \(-0.473333\pi\) | ||||
0.0836799 | + | 0.996493i | \(0.473333\pi\) | |||||||
\(242\) | −74.0667 | − | 74.0667i | −0.306061 | − | 0.306061i | ||||
\(243\) | 225.933 | − | 225.933i | 0.929766 | − | 0.929766i | ||||
\(244\) | − | 173.933i | − | 0.712841i | ||||||
\(245\) | −7.90420 | + | 34.0958i | −0.0322620 | + | 0.139167i | ||||
\(246\) | 170.383 | 0.692615 | ||||||||
\(247\) | 94.2831 | + | 94.2831i | 0.381713 | + | 0.381713i | ||||
\(248\) | 1.55006 | − | 1.55006i | 0.00625022 | − | 0.00625022i | ||||
\(249\) | − | 453.399i | − | 1.82088i | ||||||
\(250\) | −18.0000 | − | 175.858i | −0.0720000 | − | 0.703432i | ||||
\(251\) | −95.1669 | −0.379151 | −0.189575 | − | 0.981866i | \(-0.560711\pi\) | ||||
−0.189575 | + | 0.981866i | \(0.560711\pi\) | |||||||
\(252\) | −28.0000 | − | 28.0000i | −0.111111 | − | 0.111111i | ||||
\(253\) | 400.958 | − | 400.958i | 1.58481 | − | 1.58481i | ||||
\(254\) | − | 128.583i | − | 0.506234i | ||||||
\(255\) | 226.412 | + | 52.4876i | 0.887891 | + | 0.205834i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 270.566 | + | 270.566i | 1.05279 | + | 1.05279i | 0.998527 | + | 0.0542599i | \(0.0172799\pi\) |
0.0542599 | + | 0.998527i | \(0.482720\pi\) | |||||||
\(258\) | −312.825 | + | 312.825i | −1.21250 | + | 1.21250i | ||||
\(259\) | − | 139.283i | − | 0.537773i | ||||||
\(260\) | 49.4833 | + | 79.3498i | 0.190320 | + | 0.305192i | ||||
\(261\) | −149.916 | −0.574391 | ||||||||
\(262\) | −146.633 | − | 146.633i | −0.559668 | − | 0.559668i | ||||
\(263\) | 183.967 | − | 183.967i | 0.699493 | − | 0.699493i | −0.264808 | − | 0.964301i | \(-0.585309\pi\) |
0.964301 | + | 0.264808i | \(0.0853087\pi\) | |||||||
\(264\) | 160.383i | 0.607512i | ||||||||
\(265\) | −106.250 | + | 66.2583i | −0.400942 | + | 0.250031i | ||||
\(266\) | −53.3498 | −0.200563 | ||||||||
\(267\) | 229.666 | + | 229.666i | 0.860173 | + | 0.860173i | ||||
\(268\) | 83.4166 | − | 83.4166i | 0.311256 | − | 0.311256i | ||||
\(269\) | 22.4994i | 0.0836411i | 0.999125 | + | 0.0418205i | \(0.0133158\pi\) | ||||
−0.999125 | + | 0.0418205i | \(0.986684\pi\) | |||||||
\(270\) | 9.83315 | − | 42.4166i | 0.0364191 | − | 0.157098i | ||||
\(271\) | −154.067 | −0.568512 | −0.284256 | − | 0.958748i | \(-0.591747\pi\) | ||||
−0.284256 | + | 0.958748i | \(0.591747\pi\) | |||||||
\(272\) | −32.3832 | − | 32.3832i | −0.119056 | − | 0.119056i | ||||
\(273\) | −71.0291 | + | 71.0291i | −0.260180 | + | 0.260180i | ||||
\(274\) | 14.6997i | 0.0536484i | ||||||||
\(275\) | −313.550 | − | 153.633i | −1.14018 | − | 0.558665i | ||||
\(276\) | −329.666 | −1.19444 | ||||||||
\(277\) | 336.041 | + | 336.041i | 1.21314 | + | 1.21314i | 0.969987 | + | 0.243157i | \(0.0781830\pi\) |
0.243157 | + | 0.969987i | \(0.421817\pi\) | |||||||
\(278\) | 53.8665 | − | 53.8665i | 0.193764 | − | 0.193764i | ||||
\(279\) | − | 5.79978i | − | 0.0207877i | ||||||
\(280\) | −36.4499 | − | 8.44994i | −0.130178 | − | 0.0301784i | ||||
\(281\) | 283.299 | 1.00818 | 0.504091 | − | 0.863650i | \(-0.331828\pi\) | ||||
0.504091 | + | 0.863650i | \(0.331828\pi\) | |||||||
\(282\) | 367.633 | + | 367.633i | 1.30366 | + | 1.30366i | ||||
\(283\) | −193.321 | + | 193.321i | −0.683112 | + | 0.683112i | −0.960700 | − | 0.277588i | \(-0.910465\pi\) |
0.277588 | + | 0.960700i | \(0.410465\pi\) | |||||||
\(284\) | − | 94.9666i | − | 0.334390i | ||||||
\(285\) | 153.158 | + | 245.600i | 0.537397 | + | 0.861753i | ||||
\(286\) | 184.708 | 0.645833 | ||||||||
\(287\) | 55.5167 | + | 55.5167i | 0.193438 | + | 0.193438i | ||||
\(288\) | 29.9333 | − | 29.9333i | 0.103935 | − | 0.103935i | ||||
\(289\) | − | 157.916i | − | 0.546422i | ||||||
\(290\) | −120.200 | + | 74.9580i | −0.414484 | + | 0.258476i | ||||
\(291\) | −324.666 | −1.11569 | ||||||||
\(292\) | 68.7664 | + | 68.7664i | 0.235501 | + | 0.235501i | ||||
\(293\) | −346.412 | + | 346.412i | −1.18229 | + | 1.18229i | −0.203146 | + | 0.979148i | \(0.565117\pi\) |
−0.979148 | + | 0.203146i | \(0.934883\pi\) | |||||||
\(294\) | − | 40.1916i | − | 0.136706i | ||||||
\(295\) | −67.8913 | + | 292.858i | −0.230140 | + | 0.992739i | ||||
\(296\) | 148.900 | 0.503040 | ||||||||
\(297\) | −60.8127 | − | 60.8127i | −0.204757 | − | 0.204757i | ||||
\(298\) | −84.6502 | + | 84.6502i | −0.284061 | + | 0.284061i | ||||
\(299\) | 379.666i | 1.26979i | ||||||||
\(300\) | 65.7417 | + | 192.058i | 0.219139 | + | 0.640194i | ||||
\(301\) | −203.858 | −0.677269 | ||||||||
\(302\) | 21.8331 | + | 21.8331i | 0.0722952 | + | 0.0722952i | ||||
\(303\) | −219.833 | + | 219.833i | −0.725522 | + | 0.725522i | ||||
\(304\) | − | 57.0334i | − | 0.187610i | ||||||
\(305\) | −423.600 | − | 98.2002i | −1.38885 | − | 0.321968i | ||||
\(306\) | −121.167 | −0.395970 | ||||||||
\(307\) | 245.512 | + | 245.512i | 0.799715 | + | 0.799715i | 0.983050 | − | 0.183336i | \(-0.0586896\pi\) |
−0.183336 | + | 0.983050i | \(0.558690\pi\) | |||||||
\(308\) | −52.2583 | + | 52.2583i | −0.169670 | + | 0.169670i | ||||
\(309\) | − | 324.666i | − | 1.05070i | ||||||
\(310\) | −2.89989 | − | 4.65017i | −0.00935448 | − | 0.0150005i | ||||
\(311\) | 325.091 | 1.04531 | 0.522655 | − | 0.852544i | \(-0.324942\pi\) | ||||
0.522655 | + | 0.852544i | \(0.324942\pi\) | |||||||
\(312\) | −75.9333 | − | 75.9333i | −0.243376 | − | 0.243376i | ||||
\(313\) | 228.012 | − | 228.012i | 0.728472 | − | 0.728472i | −0.241843 | − | 0.970315i | \(-0.577752\pi\) |
0.970315 | + | 0.241843i | \(0.0777519\pi\) | |||||||
\(314\) | − | 69.6663i | − | 0.221867i | ||||||
\(315\) | −84.0000 | + | 52.3832i | −0.266667 | + | 0.166296i | ||||
\(316\) | 18.2670 | 0.0578068 | ||||||||
\(317\) | −314.800 | − | 314.800i | −0.993059 | − | 0.993059i | 0.00691684 | − | 0.999976i | \(-0.497798\pi\) |
−0.999976 | + | 0.00691684i | \(0.997798\pi\) | |||||||
\(318\) | 101.675 | − | 101.675i | 0.319732 | − | 0.319732i | ||||
\(319\) | 279.799i | 0.877112i | ||||||||
\(320\) | 9.03337 | − | 38.9666i | 0.0282293 | − | 0.121771i | ||||
\(321\) | −157.225 | −0.489797 | ||||||||
\(322\) | −107.417 | − | 107.417i | −0.333592 | − | 0.333592i | ||||
\(323\) | −115.433 | + | 115.433i | −0.357377 | + | 0.357377i | ||||
\(324\) | 184.700i | 0.570061i | ||||||||
\(325\) | 221.187 | − | 75.7126i | 0.680576 | − | 0.232962i | ||||
\(326\) | 90.4499 | 0.277454 | ||||||||
\(327\) | −444.595 | − | 444.595i | −1.35962 | − | 1.35962i | ||||
\(328\) | −59.3498 | + | 59.3498i | −0.180945 | + | 0.180945i | ||||
\(329\) | 239.575i | 0.728191i | ||||||||
\(330\) | 390.600 | + | 90.5501i | 1.18364 | + | 0.274394i | ||||
\(331\) | −65.2831 | −0.197230 | −0.0986149 | − | 0.995126i | \(-0.531441\pi\) | ||||
−0.0986149 | + | 0.995126i | \(0.531441\pi\) | |||||||
\(332\) | 157.933 | + | 157.933i | 0.475703 | + | 0.475703i | ||||
\(333\) | 278.566 | − | 278.566i | 0.836535 | − | 0.836535i | ||||
\(334\) | 156.075i | 0.467292i | ||||||||
\(335\) | −156.058 | − | 250.250i | −0.465845 | − | 0.747014i | ||||
\(336\) | 42.9666 | 0.127877 | ||||||||
\(337\) | −18.0086 | − | 18.0086i | −0.0534380 | − | 0.0534380i | 0.679883 | − | 0.733321i | \(-0.262031\pi\) |
−0.733321 | + | 0.679883i | \(0.762031\pi\) | |||||||
\(338\) | 81.5501 | − | 81.5501i | 0.241272 | − | 0.241272i | ||||
\(339\) | − | 568.566i | − | 1.67719i | ||||||
\(340\) | −97.1496 | + | 60.5834i | −0.285734 | + | 0.178187i | ||||
\(341\) | −10.8245 | −0.0317435 | ||||||||
\(342\) | −106.700 | − | 106.700i | −0.311987 | − | 0.311987i | ||||
\(343\) | 13.0958 | − | 13.0958i | 0.0381802 | − | 0.0381802i | ||||
\(344\) | − | 217.933i | − | 0.633527i | ||||||
\(345\) | −186.125 | + | 802.874i | −0.539492 | + | 2.32717i | ||||
\(346\) | 204.174 | 0.590099 | ||||||||
\(347\) | 137.625 | + | 137.625i | 0.396615 | + | 0.396615i | 0.877037 | − | 0.480422i | \(-0.159517\pi\) |
−0.480422 | + | 0.877037i | \(0.659517\pi\) | |||||||
\(348\) | 115.025 | − | 115.025i | 0.330531 | − | 0.330531i | ||||
\(349\) | 496.174i | 1.42170i | 0.703342 | + | 0.710852i | \(0.251690\pi\) | ||||
−0.703342 | + | 0.710852i | \(0.748310\pi\) | |||||||
\(350\) | −41.1582 | + | 84.0000i | −0.117595 | + | 0.240000i | ||||
\(351\) | 57.5834 | 0.164055 | ||||||||
\(352\) | −55.8665 | − | 55.8665i | −0.158712 | − | 0.158712i | ||||
\(353\) | 92.1625 | − | 92.1625i | 0.261084 | − | 0.261084i | −0.564411 | − | 0.825494i | \(-0.690896\pi\) |
0.825494 | + | 0.564411i | \(0.190896\pi\) | |||||||
\(354\) | − | 345.216i | − | 0.975187i | ||||||
\(355\) | −231.283 | − | 53.6168i | −0.651502 | − | 0.151033i | ||||
\(356\) | −160.000 | −0.449438 | ||||||||
\(357\) | −86.9623 | − | 86.9623i | −0.243592 | − | 0.243592i | ||||
\(358\) | 248.250 | − | 248.250i | 0.693435 | − | 0.693435i | ||||
\(359\) | − | 592.232i | − | 1.64967i | −0.565372 | − | 0.824836i | \(-0.691267\pi\) | ||
0.565372 | − | 0.824836i | \(-0.308733\pi\) | |||||||
\(360\) | −56.0000 | − | 89.7998i | −0.155556 | − | 0.249444i | ||||
\(361\) | 157.700 | 0.436841 | ||||||||
\(362\) | 17.1582 | + | 17.1582i | 0.0473984 | + | 0.0473984i | ||||
\(363\) | 212.633 | − | 212.633i | 0.585766 | − | 0.585766i | ||||
\(364\) | − | 49.4833i | − | 0.135943i | ||||||
\(365\) | 206.299 | − | 128.650i | 0.565203 | − | 0.352466i | ||||
\(366\) | 499.333 | 1.36430 | ||||||||
\(367\) | 42.0872 | + | 42.0872i | 0.114679 | + | 0.114679i | 0.762118 | − | 0.647439i | \(-0.224160\pi\) |
−0.647439 | + | 0.762118i | \(0.724160\pi\) | |||||||
\(368\) | 114.833 | − | 114.833i | 0.312047 | − | 0.312047i | ||||
\(369\) | 222.067i | 0.601807i | ||||||||
\(370\) | 84.0667 | − | 362.633i | 0.227207 | − | 0.980089i | ||||
\(371\) | 66.2583 | 0.178594 | ||||||||
\(372\) | 4.44994 | + | 4.44994i | 0.0119622 | + | 0.0119622i | ||||
\(373\) | −160.133 | + | 160.133i | −0.429312 | + | 0.429312i | −0.888394 | − | 0.459082i | \(-0.848178\pi\) |
0.459082 | + | 0.888394i | \(0.348178\pi\) | |||||||
\(374\) | 226.142i | 0.604658i | ||||||||
\(375\) | 504.858 | − | 51.6749i | 1.34629 | − | 0.137800i | ||||
\(376\) | −256.116 | −0.681160 | ||||||||
\(377\) | −132.470 | − | 132.470i | −0.351380 | − | 0.351380i | ||||
\(378\) | −16.2917 | + | 16.2917i | −0.0430998 | + | 0.0430998i | ||||
\(379\) | 749.066i | 1.97643i | 0.153084 | + | 0.988213i | \(0.451080\pi\) | ||||
−0.153084 | + | 0.988213i | \(0.548920\pi\) | |||||||
\(380\) | −138.900 | − | 32.2002i | −0.365526 | − | 0.0847374i | ||||
\(381\) | 369.141 | 0.968874 | ||||||||
\(382\) | −200.916 | − | 200.916i | −0.525958 | − | 0.525958i | ||||
\(383\) | −295.399 | + | 295.399i | −0.771278 | + | 0.771278i | −0.978330 | − | 0.207052i | \(-0.933613\pi\) |
0.207052 | + | 0.978330i | \(0.433613\pi\) | |||||||
\(384\) | 45.9333i | 0.119618i | ||||||||
\(385\) | 97.7664 | + | 156.775i | 0.253939 | + | 0.407208i | ||||
\(386\) | −243.600 | −0.631087 | ||||||||
\(387\) | −407.716 | − | 407.716i | −1.05353 | − | 1.05353i | ||||
\(388\) | 113.091 | − | 113.091i | 0.291473 | − | 0.291473i | ||||
\(389\) | 387.116i | 0.995157i | 0.867419 | + | 0.497579i | \(0.165777\pi\) | ||||
−0.867419 | + | 0.497579i | \(0.834223\pi\) | |||||||
\(390\) | −227.800 | + | 142.058i | −0.584102 | + | 0.364252i | ||||
\(391\) | −464.833 | −1.18883 | ||||||||
\(392\) | 14.0000 | + | 14.0000i | 0.0357143 | + | 0.0357143i | ||||
\(393\) | 420.958 | − | 420.958i | 1.07114 | − | 1.07114i | ||||
\(394\) | 430.250i | 1.09200i | ||||||||
\(395\) | 10.3133 | − | 44.4876i | 0.0261095 | − | 0.112627i | ||||
\(396\) | −209.033 | −0.527862 | ||||||||
\(397\) | −282.203 | − | 282.203i | −0.710840 | − | 0.710840i | 0.255871 | − | 0.966711i | \(-0.417638\pi\) |
−0.966711 | + | 0.255871i | \(0.917638\pi\) | |||||||
\(398\) | −93.2917 | + | 93.2917i | −0.234401 | + | 0.234401i | ||||
\(399\) | − | 153.158i | − | 0.383855i | ||||||
\(400\) | −89.7998 | − | 44.0000i | −0.224499 | − | 0.110000i | ||||
\(401\) | −95.6502 | −0.238529 | −0.119265 | − | 0.992863i | \(-0.538054\pi\) | ||||
−0.119265 | + | 0.992863i | \(0.538054\pi\) | |||||||
\(402\) | 239.475 | + | 239.475i | 0.595708 | + | 0.595708i | ||||
\(403\) | 5.12486 | − | 5.12486i | 0.0127168 | − | 0.0127168i | ||||
\(404\) | − | 153.150i | − | 0.379083i | ||||||
\(405\) | 449.820 | + | 104.279i | 1.11067 | + | 0.257478i | ||||
\(406\) | 74.9580 | 0.184626 | ||||||||
\(407\) | −519.907 | − | 519.907i | −1.27741 | − | 1.27741i | ||||
\(408\) | 92.9666 | − | 92.9666i | 0.227859 | − | 0.227859i | ||||
\(409\) | − | 113.875i | − | 0.278423i | −0.990263 | − | 0.139212i | \(-0.955543\pi\) | ||
0.990263 | − | 0.139212i | \(-0.0444568\pi\) | |||||||
\(410\) | 111.033 | + | 178.049i | 0.270813 | + | 0.434267i | ||||
\(411\) | −42.2002 | −0.102677 | ||||||||
\(412\) | 113.091 | + | 113.091i | 0.274494 | + | 0.274494i | ||||
\(413\) | 112.483 | − | 112.483i | 0.272357 | − | 0.272357i | ||||
\(414\) | − | 429.666i | − | 1.03784i | ||||||
\(415\) | 473.800 | − | 295.466i | 1.14169 | − | 0.711966i | ||||
\(416\) | 52.8999 | 0.127163 | ||||||||
\(417\) | 154.642 | + | 154.642i | 0.370843 | + | 0.370843i | ||||
\(418\) | −199.141 | + | 199.141i | −0.476414 | + | 0.476414i | ||||
\(419\) | − | 445.158i | − | 1.06243i | −0.847237 | − | 0.531215i | \(-0.821736\pi\) | ||
0.847237 | − | 0.531215i | \(-0.178264\pi\) | |||||||
\(420\) | 24.2583 | − | 104.642i | 0.0577580 | − | 0.249147i | ||||
\(421\) | 164.333 | 0.390339 | 0.195169 | − | 0.980770i | \(-0.437474\pi\) | ||||
0.195169 | + | 0.980770i | \(0.437474\pi\) | |||||||
\(422\) | 74.3498 | + | 74.3498i | 0.176184 | + | 0.176184i | ||||
\(423\) | −479.150 | + | 479.150i | −1.13274 | + | 1.13274i | ||||
\(424\) | 70.8331i | 0.167059i | ||||||||
\(425\) | 92.6965 | + | 270.804i | 0.218109 | + | 0.637186i | ||||
\(426\) | 272.633 | 0.639983 | ||||||||
\(427\) | 162.700 | + | 162.700i | 0.381030 | + | 0.381030i | ||||
\(428\) | 54.7664 | − | 54.7664i | 0.127959 | − | 0.127959i | ||||
\(429\) | 530.266i | 1.23605i | ||||||||
\(430\) | −530.758 | − | 123.042i | −1.23432 | − | 0.286144i | ||||
\(431\) | 466.199 | 1.08167 | 0.540834 | − | 0.841129i | \(-0.318109\pi\) | ||||
0.540834 | + | 0.841129i | \(0.318109\pi\) | |||||||
\(432\) | −17.4166 | − | 17.4166i | −0.0403161 | − | 0.0403161i | ||||
\(433\) | 221.274 | − | 221.274i | 0.511026 | − | 0.511026i | −0.403814 | − | 0.914841i | \(-0.632316\pi\) |
0.914841 | + | 0.403814i | \(0.132316\pi\) | |||||||
\(434\) | 2.89989i | 0.00668177i | ||||||||
\(435\) | −215.192 | − | 345.074i | −0.494693 | − | 0.793274i | ||||
\(436\) | 309.733 | 0.710397 | ||||||||
\(437\) | −409.333 | − | 409.333i | −0.936688 | − | 0.936688i | ||||
\(438\) | −197.417 | + | 197.417i | −0.450723 | + | 0.450723i | ||||
\(439\) | 32.5662i | 0.0741827i | 0.999312 | + | 0.0370913i | \(0.0118092\pi\) | ||||
−0.999312 | + | 0.0370913i | \(0.988191\pi\) | |||||||
\(440\) | −167.600 | + | 104.517i | −0.380908 | + | 0.237538i | ||||
\(441\) | 52.3832 | 0.118783 | ||||||||
\(442\) | −107.067 | − | 107.067i | −0.242232 | − | 0.242232i | ||||
\(443\) | 312.849 | − | 312.849i | 0.706206 | − | 0.706206i | −0.259529 | − | 0.965735i | \(-0.583567\pi\) |
0.965735 | + | 0.259529i | \(0.0835674\pi\) | |||||||
\(444\) | 427.466i | 0.962761i | ||||||||
\(445\) | −90.3337 | + | 389.666i | −0.202997 | + | 0.875655i | ||||
\(446\) | 225.858 | 0.506408 | ||||||||
\(447\) | −243.016 | − | 243.016i | −0.543660 | − | 0.543660i | ||||
\(448\) | −14.9666 | + | 14.9666i | −0.0334077 | + | 0.0334077i | ||||
\(449\) | 276.582i | 0.615996i | 0.951387 | + | 0.307998i | \(0.0996591\pi\) | ||||
−0.951387 | + | 0.307998i | \(0.900341\pi\) | |||||||
\(450\) | −250.316 | + | 85.6835i | −0.556259 | + | 0.190408i | ||||
\(451\) | 414.459 | 0.918977 | ||||||||
\(452\) | 198.049 | + | 198.049i | 0.438163 | + | 0.438163i | ||||
\(453\) | −62.6792 | + | 62.6792i | −0.138365 | + | 0.138365i | ||||
\(454\) | − | 171.559i | − | 0.377883i | ||||||
\(455\) | −120.512 | − | 27.9376i | −0.264862 | − | 0.0614013i | ||||
\(456\) | 163.733 | 0.359064 | ||||||||
\(457\) | 77.4413 | + | 77.4413i | 0.169456 | + | 0.169456i | 0.786740 | − | 0.617284i | \(-0.211767\pi\) |
−0.617284 | + | 0.786740i | \(0.711767\pi\) | |||||||
\(458\) | 215.875 | − | 215.875i | 0.471343 | − | 0.471343i | ||||
\(459\) | 70.5006i | 0.153596i | ||||||||
\(460\) | −214.833 | − | 344.499i | −0.467029 | − | 0.748912i | ||||
\(461\) | −615.600 | −1.33536 | −0.667678 | − | 0.744450i | \(-0.732712\pi\) | ||||
−0.667678 | + | 0.744450i | \(0.732712\pi\) | |||||||
\(462\) | −150.025 | − | 150.025i | −0.324729 | − | 0.324729i | ||||
\(463\) | 146.566 | − | 146.566i | 0.316558 | − | 0.316558i | −0.530886 | − | 0.847443i | \(-0.678141\pi\) |
0.847443 | + | 0.530886i | \(0.178141\pi\) | |||||||
\(464\) | 80.1335i | 0.172701i | ||||||||
\(465\) | 13.3498 | − | 8.32508i | 0.0287093 | − | 0.0179034i | ||||
\(466\) | 155.100 | 0.332833 | ||||||||
\(467\) | −95.0711 | − | 95.0711i | −0.203578 | − | 0.203578i | 0.597953 | − | 0.801531i | \(-0.295981\pi\) |
−0.801531 | + | 0.597953i | \(0.795981\pi\) | |||||||
\(468\) | 98.9666 | − | 98.9666i | 0.211467 | − | 0.211467i | ||||
\(469\) | 156.058i | 0.332747i | ||||||||
\(470\) | −144.600 | + | 623.749i | −0.307659 | + | 1.32713i | ||||
\(471\) | 200.000 | 0.424628 | ||||||||
\(472\) | 120.250 | + | 120.250i | 0.254766 | + | 0.254766i | ||||
\(473\) | −760.948 | + | 760.948i | −1.60877 | + | 1.60877i | ||||
\(474\) | 52.4413i | 0.110636i | ||||||||
\(475\) | −156.842 | + | 320.099i | −0.330193 | + | 0.673893i | ||||
\(476\) | 60.5834 | 0.127276 | ||||||||
\(477\) | 132.517 | + | 132.517i | 0.277813 | + | 0.277813i | ||||
\(478\) | −30.4661 | + | 30.4661i | −0.0637366 | + | 0.0637366i | ||||
\(479\) | 32.0667i | 0.0669452i | 0.999440 | + | 0.0334726i | \(0.0106566\pi\) | ||||
−0.999440 | + | 0.0334726i | \(0.989343\pi\) | |||||||
\(480\) | 111.867 | + | 25.9333i | 0.233055 | + | 0.0540276i | ||||
\(481\) | 492.299 | 1.02349 | ||||||||
\(482\) | −40.3337 | − | 40.3337i | −0.0836799 | − | 0.0836799i | ||||
\(483\) | 308.375 | − | 308.375i | 0.638457 | − | 0.638457i | ||||
\(484\) | 148.133i | 0.306061i | ||||||||
\(485\) | −211.575 | − | 339.274i | −0.436237 | − | 0.699535i | ||||
\(486\) | −451.867 | −0.929766 | ||||||||
\(487\) | −449.324 | − | 449.324i | −0.922636 | − | 0.922636i | 0.0745786 | − | 0.997215i | \(-0.476239\pi\) |
−0.997215 | + | 0.0745786i | \(0.976239\pi\) | |||||||
\(488\) | −173.933 | + | 173.933i | −0.356421 | + | 0.356421i | ||||
\(489\) | 259.666i | 0.531015i | ||||||||
\(490\) | 42.0000 | − | 26.1916i | 0.0857143 | − | 0.0534522i | ||||
\(491\) | 322.216 | 0.656245 | 0.328123 | − | 0.944635i | \(-0.393584\pi\) | ||||
0.328123 | + | 0.944635i | \(0.393584\pi\) | |||||||
\(492\) | −170.383 | − | 170.383i | −0.346307 | − | 0.346307i | ||||
\(493\) | 162.186 | − | 162.186i | 0.328978 | − | 0.328978i | ||||
\(494\) | − | 188.566i | − | 0.381713i | ||||||
\(495\) | −118.017 | + | 509.083i | −0.238419 | + | 1.02845i | ||||
\(496\) | −3.10011 | −0.00625022 | ||||||||
\(497\) | 88.8331 | + | 88.8331i | 0.178739 | + | 0.178739i | ||||
\(498\) | −453.399 | + | 453.399i | −0.910440 | + | 0.910440i | ||||
\(499\) | 925.648i | 1.85501i | 0.373816 | + | 0.927503i | \(0.378049\pi\) | ||||
−0.373816 | + | 0.927503i | \(0.621951\pi\) | |||||||
\(500\) | −157.858 | + | 193.858i | −0.315716 | + | 0.387716i | ||||
\(501\) | −448.066 | −0.894343 | ||||||||
\(502\) | 95.1669 | + | 95.1669i | 0.189575 | + | 0.189575i | ||||
\(503\) | 158.029 | − | 158.029i | 0.314173 | − | 0.314173i | −0.532351 | − | 0.846524i | \(-0.678691\pi\) |
0.846524 | + | 0.532351i | \(0.178691\pi\) | |||||||
\(504\) | 56.0000i | 0.111111i | ||||||||
\(505\) | −372.983 | − | 86.4661i | −0.738580 | − | 0.171220i | ||||
\(506\) | −801.916 | −1.58481 | ||||||||
\(507\) | 234.116 | + | 234.116i | 0.461768 | + | 0.461768i | ||||
\(508\) | −128.583 | + | 128.583i | −0.253117 | + | 0.253117i | ||||
\(509\) | − | 972.299i | − | 1.91021i | −0.296260 | − | 0.955107i | \(-0.595740\pi\) | ||
0.296260 | − | 0.955107i | \(-0.404260\pi\) | |||||||
\(510\) | −173.925 | − | 278.900i | −0.341029 | − | 0.546863i | ||||
\(511\) | −128.650 | −0.251762 | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −62.0829 | + | 62.0829i | −0.121019 | + | 0.121019i | ||||
\(514\) | − | 541.132i | − | 1.05279i | ||||||
\(515\) | 339.274 | − | 211.575i | 0.658785 | − | 0.410825i | ||||
\(516\) | 625.649 | 1.21250 | ||||||||
\(517\) | 894.270 | + | 894.270i | 1.72973 | + | 1.72973i | ||||
\(518\) | −139.283 | + | 139.283i | −0.268886 | + | 0.268886i | ||||
\(519\) | 586.150i | 1.12938i | ||||||||
\(520\) | 29.8665 | − | 128.833i | 0.0574356 | − | 0.247756i | ||||
\(521\) | −178.525 | −0.342659 | −0.171329 | − | 0.985214i | \(-0.554806\pi\) | ||||
−0.171329 | + | 0.985214i | \(0.554806\pi\) | |||||||
\(522\) | 149.916 | + | 149.916i | 0.287195 | + | 0.287195i | ||||
\(523\) | 412.241 | − | 412.241i | 0.788224 | − | 0.788224i | −0.192979 | − | 0.981203i | \(-0.561815\pi\) |
0.981203 | + | 0.192979i | \(0.0618149\pi\) | |||||||
\(524\) | 293.266i | 0.559668i | ||||||||
\(525\) | −241.150 | − | 118.158i | −0.459333 | − | 0.225063i | ||||
\(526\) | −367.933 | −0.699493 | ||||||||
\(527\) | 6.27447 | + | 6.27447i | 0.0119060 | + | 0.0119060i | ||||
\(528\) | 160.383 | − | 160.383i | 0.303756 | − | 0.303756i | ||||
\(529\) | − | 1119.33i | − | 2.11594i | ||||||
\(530\) | 172.508 | + | 39.9914i | 0.325487 | + | 0.0754554i | ||||
\(531\) | 449.933 | 0.847332 | ||||||||
\(532\) | 53.3498 | + | 53.3498i | 0.100282 | + | 0.100282i | ||||
\(533\) | −196.225 | + | 196.225i | −0.368152 | + | 0.368152i | ||||
\(534\) | − | 459.333i | − | 0.860173i | ||||||
\(535\) | −102.459 | − | 164.299i | −0.191511 | − | 0.307101i | ||||
\(536\) | −166.833 | −0.311256 | ||||||||
\(537\) | 712.682 | + | 712.682i | 1.32716 | + | 1.32716i | ||||
\(538\) | 22.4994 | − | 22.4994i | 0.0418205 | − | 0.0418205i | ||||
\(539\) | − | 97.7664i | − | 0.181385i | ||||||
\(540\) | −52.2497 | + | 32.5834i | −0.0967587 | + | 0.0603397i | ||||
\(541\) | 485.133 | 0.896735 | 0.448367 | − | 0.893849i | \(-0.352006\pi\) | ||||
0.448367 | + | 0.893849i | \(0.352006\pi\) | |||||||
\(542\) | 154.067 | + | 154.067i | 0.284256 | + | 0.284256i | ||||
\(543\) | −49.2583 | + | 49.2583i | −0.0907152 | + | 0.0907152i | ||||
\(544\) | 64.7664i | 0.119056i | ||||||||
\(545\) | 174.871 | − | 754.328i | 0.320864 | − | 1.38409i | ||||
\(546\) | 142.058 | 0.260180 | ||||||||
\(547\) | 92.0172 | + | 92.0172i | 0.168222 | + | 0.168222i | 0.786197 | − | 0.617976i | \(-0.212047\pi\) |
−0.617976 | + | 0.786197i | \(0.712047\pi\) | |||||||
\(548\) | 14.6997 | − | 14.6997i | 0.0268242 | − | 0.0268242i | ||||
\(549\) | 650.799i | 1.18543i | ||||||||
\(550\) | 159.917 | + | 467.183i | 0.290758 | + | 0.849424i | ||||
\(551\) | 285.643 | 0.518408 | ||||||||
\(552\) | 329.666 | + | 329.666i | 0.597222 | + | 0.597222i | ||||
\(553\) | −17.0872 | + | 17.0872i | −0.0308991 | + | 0.0308991i | ||||
\(554\) | − | 672.082i | − | 1.21314i | ||||||
\(555\) | 1041.06 | + | 241.341i | 1.87578 | + | 0.434849i | ||||
\(556\) | −107.733 | −0.193764 | ||||||||
\(557\) | −201.283 | − | 201.283i | −0.361370 | − | 0.361370i | 0.502947 | − | 0.864317i | \(-0.332249\pi\) |
−0.864317 | + | 0.502947i | \(0.832249\pi\) | |||||||
\(558\) | −5.79978 | + | 5.79978i | −0.0103939 | + | 0.0103939i | ||||
\(559\) | − | 720.540i | − | 1.28898i | ||||||
\(560\) | 28.0000 | + | 44.8999i | 0.0500000 | + | 0.0801784i | ||||
\(561\) | −649.215 | −1.15725 | ||||||||
\(562\) | −283.299 | − | 283.299i | −0.504091 | − | 0.504091i | ||||
\(563\) | −200.949 | + | 200.949i | −0.356926 | + | 0.356926i | −0.862679 | − | 0.505753i | \(-0.831215\pi\) |
0.505753 | + | 0.862679i | \(0.331215\pi\) | |||||||
\(564\) | − | 735.266i | − | 1.30366i | ||||||
\(565\) | 594.148 | − | 370.517i | 1.05159 | − | 0.655782i | ||||
\(566\) | 386.642 | 0.683112 | ||||||||
\(567\) | −172.771 | − | 172.771i | −0.304710 | − | 0.304710i | ||||
\(568\) | −94.9666 | + | 94.9666i | −0.167195 | + | 0.167195i | ||||
\(569\) | − | 724.349i | − | 1.27302i | −0.771268 | − | 0.636510i | \(-0.780377\pi\) | ||
0.771268 | − | 0.636510i | \(-0.219623\pi\) | |||||||
\(570\) | 92.4413 | − | 398.758i | 0.162178 | − | 0.699575i | ||||
\(571\) | −650.850 | −1.13984 | −0.569922 | − | 0.821699i | \(-0.693026\pi\) | ||||
−0.569922 | + | 0.821699i | \(0.693026\pi\) | |||||||
\(572\) | −184.708 | − | 184.708i | −0.322917 | − | 0.322917i | ||||
\(573\) | 576.795 | − | 576.795i | 1.00662 | − | 1.00662i | ||||
\(574\) | − | 111.033i | − | 0.193438i | ||||||
\(575\) | −960.291 | + | 328.708i | −1.67007 | + | 0.571667i | ||||
\(576\) | −59.8665 | −0.103935 | ||||||||
\(577\) | −758.711 | − | 758.711i | −1.31492 | − | 1.31492i | −0.917738 | − | 0.397187i | \(-0.869987\pi\) |
−0.397187 | − | 0.917738i | \(-0.630013\pi\) | |||||||
\(578\) | −157.916 | + | 157.916i | −0.273211 | + | 0.273211i | ||||
\(579\) | − | 699.333i | − | 1.20783i | ||||||
\(580\) | 195.158 | + | 45.2422i | 0.336480 | + | 0.0780038i | ||||
\(581\) | −295.466 | −0.508547 | ||||||||
\(582\) | 324.666 | + | 324.666i | 0.557846 | + | 0.557846i | ||||
\(583\) | 247.325 | − | 247.325i | 0.424228 | − | 0.424228i | ||||
\(584\) | − | 137.533i | − | 0.235501i | ||||||
\(585\) | −185.150 | − | 296.900i | −0.316495 | − | 0.507521i | ||||
\(586\) | 692.825 | 1.18229 | ||||||||
\(587\) | 422.865 | + | 422.865i | 0.720384 | + | 0.720384i | 0.968683 | − | 0.248299i | \(-0.0798717\pi\) |
−0.248299 | + | 0.968683i | \(0.579872\pi\) | |||||||
\(588\) | −40.1916 | + | 40.1916i | −0.0683531 | + | 0.0683531i | ||||
\(589\) | 11.0506i | 0.0187617i | ||||||||
\(590\) | 360.749 | − | 224.967i | 0.611439 | − | 0.381299i | ||||
\(591\) | −1235.17 | −2.08997 | ||||||||
\(592\) | −148.900 | − | 148.900i | −0.251520 | − | 0.251520i | ||||
\(593\) | −633.245 | + | 633.245i | −1.06787 | + | 1.06787i | −0.0703447 | + | 0.997523i | \(0.522410\pi\) |
−0.997523 | + | 0.0703447i | \(0.977590\pi\) | |||||||
\(594\) | 121.625i | 0.204757i | ||||||||
\(595\) | 34.2045 | − | 147.546i | 0.0574866 | − | 0.247976i | ||||
\(596\) | 169.300 | 0.284061 | ||||||||
\(597\) | −267.825 | − | 267.825i | −0.448617 | − | 0.448617i | ||||
\(598\) | 379.666 | − | 379.666i | 0.634893 | − | 0.634893i | ||||
\(599\) | 688.733i | 1.14980i | 0.818222 | + | 0.574902i | \(0.194960\pi\) | ||||
−0.818222 | + | 0.574902i | \(0.805040\pi\) | |||||||
\(600\) | 126.316 | − | 257.800i | 0.210527 | − | 0.429666i | ||||
\(601\) | −651.739 | −1.08443 | −0.542213 | − | 0.840241i | \(-0.682413\pi\) | ||||
−0.542213 | + | 0.840241i | \(0.682413\pi\) | |||||||
\(602\) | 203.858 | + | 203.858i | 0.338634 | + | 0.338634i | ||||
\(603\) | −312.116 | + | 312.116i | −0.517606 | + | 0.517606i | ||||
\(604\) | − | 43.6663i | − | 0.0722952i | ||||||
\(605\) | 360.766 | + | 83.6340i | 0.596308 | + | 0.138238i | ||||
\(606\) | 439.666 | 0.725522 | ||||||||
\(607\) | 203.678 | + | 203.678i | 0.335549 | + | 0.335549i | 0.854689 | − | 0.519140i | \(-0.173748\pi\) |
−0.519140 | + | 0.854689i | \(0.673748\pi\) | |||||||
\(608\) | −57.0334 | + | 57.0334i | −0.0938049 | + | 0.0938049i | ||||
\(609\) | 215.192i | 0.353352i | ||||||||
\(610\) | 325.399 | + | 521.800i | 0.533442 | + | 0.855409i | ||||
\(611\) | −846.783 | −1.38590 | ||||||||
\(612\) | 121.167 | + | 121.167i | 0.197985 | + | 0.197985i | ||||
\(613\) | 357.766 | − | 357.766i | 0.583632 | − | 0.583632i | −0.352267 | − | 0.935899i | \(-0.614589\pi\) |
0.935899 | + | 0.352267i | \(0.114589\pi\) | |||||||
\(614\) | − | 491.025i | − | 0.799715i | ||||||
\(615\) | −511.150 | + | 318.758i | −0.831138 | + | 0.518305i | ||||
\(616\) | 104.517 | 0.169670 | ||||||||
\(617\) | 328.174 | + | 328.174i | 0.531887 | + | 0.531887i | 0.921134 | − | 0.389246i | \(-0.127265\pi\) |
−0.389246 | + | 0.921134i | \(0.627265\pi\) | |||||||
\(618\) | −324.666 | + | 324.666i | −0.525350 | + | 0.525350i | ||||
\(619\) | 949.733i | 1.53430i | 0.641466 | + | 0.767151i | \(0.278326\pi\) | ||||
−0.641466 | + | 0.767151i | \(0.721674\pi\) | |||||||
\(620\) | −1.75028 | + | 7.55006i | −0.00282303 | + | 0.0121775i | ||||
\(621\) | −250.000 | −0.402576 | ||||||||
\(622\) | −325.091 | − | 325.091i | −0.522655 | − | 0.522655i | ||||
\(623\) | 149.666 | − | 149.666i | 0.240235 | − | 0.240235i | ||||
\(624\) | 151.867i | 0.243376i | ||||||||
\(625\) | 383.000 | + | 493.899i | 0.612800 | + | 0.790238i | ||||
\(626\) | −456.024 | −0.728472 | ||||||||
\(627\) | −571.700 | − | 571.700i | −0.911802 | − | 0.911802i | ||||
\(628\) | −69.6663 | + | 69.6663i | −0.110934 | + | 0.110934i | ||||
\(629\) | 602.732i | 0.958238i | ||||||||
\(630\) | 136.383 | + | 31.6168i | 0.216481 | + | 0.0501854i | ||||
\(631\) | −646.266 | −1.02419 | −0.512097 | − | 0.858928i | \(-0.671131\pi\) | ||||
−0.512097 | + | 0.858928i | \(0.671131\pi\) | |||||||
\(632\) | −18.2670 | − | 18.2670i | −0.0289034 | − | 0.0289034i | ||||
\(633\) | −213.446 | + | 213.446i | −0.337197 | + | 0.337197i | ||||
\(634\) | 629.600i | 0.993059i | ||||||||
\(635\) | 240.558 | + | 385.750i | 0.378831 | + | 0.607481i | ||||
\(636\) | −203.350 | −0.319732 | ||||||||
\(637\) | 46.2874 | + | 46.2874i | 0.0726647 | + | 0.0726647i | ||||
\(638\) | 279.799 | − | 279.799i | 0.438556 | − | 0.438556i | ||||
\(639\) | 355.333i | 0.556076i | ||||||||
\(640\) | −48.0000 | + | 29.9333i | −0.0750000 | + | 0.0467707i | ||||
\(641\) | 409.899 | 0.639468 | 0.319734 | − | 0.947507i | \(-0.396407\pi\) | ||||
0.319734 | + | 0.947507i | \(0.396407\pi\) | |||||||
\(642\) | 157.225 | + | 157.225i | 0.244899 | + | 0.244899i | ||||
\(643\) | −125.487 | + | 125.487i | −0.195158 | + | 0.195158i | −0.797921 | − | 0.602763i | \(-0.794067\pi\) |
0.602763 | + | 0.797921i | \(0.294067\pi\) | |||||||
\(644\) | 214.833i | 0.333592i | ||||||||
\(645\) | 353.232 | − | 1523.71i | 0.547647 | − | 2.36235i | ||||
\(646\) | 230.865 | 0.357377 | ||||||||
\(647\) | 694.291 | + | 694.291i | 1.07309 | + | 1.07309i | 0.997109 | + | 0.0759830i | \(0.0242095\pi\) |
0.0759830 | + | 0.997109i | \(0.475791\pi\) | |||||||
\(648\) | 184.700 | − | 184.700i | 0.285030 | − | 0.285030i | ||||
\(649\) | − | 839.742i | − | 1.29390i | ||||||
\(650\) | −296.900 | − | 145.475i | −0.456769 | − | 0.223807i | ||||
\(651\) | −8.32508 | −0.0127881 | ||||||||
\(652\) | −90.4499 | − | 90.4499i | −0.138727 | − | 0.138727i | ||||
\(653\) | 187.784 | − | 187.784i | 0.287571 | − | 0.287571i | −0.548548 | − | 0.836119i | \(-0.684819\pi\) |
0.836119 | + | 0.548548i | \(0.184819\pi\) | |||||||
\(654\) | 889.190i | 1.35962i | ||||||||
\(655\) | 714.224 | + | 165.574i | 1.09042 | + | 0.252784i | ||||
\(656\) | 118.700 | 0.180945 | ||||||||
\(657\) | −257.300 | − | 257.300i | −0.391629 | − | 0.391629i | ||||
\(658\) | 239.575 | − | 239.575i | 0.364095 | − | 0.364095i | ||||
\(659\) | − | 144.983i | − | 0.220004i | −0.993931 | − | 0.110002i | \(-0.964914\pi\) | ||
0.993931 | − | 0.110002i | \(-0.0350858\pi\) | |||||||
\(660\) | −300.049 | − | 481.150i | −0.454620 | − | 0.729015i | ||||
\(661\) | −433.266 | −0.655470 | −0.327735 | − | 0.944770i | \(-0.606285\pi\) | ||||
−0.327735 | + | 0.944770i | \(0.606285\pi\) | |||||||
\(662\) | 65.2831 | + | 65.2831i | 0.0986149 | + | 0.0986149i | ||||
\(663\) | 307.370 | − | 307.370i | 0.463605 | − | 0.463605i | ||||
\(664\) | − | 315.867i | − | 0.475703i | ||||||
\(665\) | 160.049 | − | 99.8084i | 0.240676 | − | 0.150088i | ||||
\(666\) | −557.132 | −0.836535 | ||||||||
\(667\) | 575.124 | + | 575.124i | 0.862254 | + | 0.862254i | ||||
\(668\) | 156.075 | − | 156.075i | 0.233646 | − | 0.233646i | ||||
\(669\) | 648.399i | 0.969207i | ||||||||
\(670\) | −94.1916 | + | 406.308i | −0.140584 | + | 0.606430i | ||||
\(671\) | 1214.63 | 1.81018 | ||||||||
\(672\) | −42.9666 | − | 42.9666i | −0.0639384 | − | 0.0639384i | ||||
\(673\) | −783.315 | + | 783.315i | −1.16392 | + | 1.16392i | −0.180305 | + | 0.983611i | \(0.557709\pi\) |
−0.983611 | + | 0.180305i | \(0.942291\pi\) | |||||||
\(674\) | 36.0172i | 0.0534380i | ||||||||
\(675\) | 49.8547 | + | 145.646i | 0.0738588 | + | 0.215772i | ||||
\(676\) | −163.100 | −0.241272 | ||||||||
\(677\) | 232.380 | + | 232.380i | 0.343250 | + | 0.343250i | 0.857588 | − | 0.514338i | \(-0.171962\pi\) |
−0.514338 | + | 0.857588i | \(0.671962\pi\) | |||||||
\(678\) | −568.566 | + | 568.566i | −0.838593 | + | 0.838593i | ||||
\(679\) | 211.575i | 0.311598i | ||||||||
\(680\) | 157.733 | + | 36.5662i | 0.231960 | + | 0.0537738i | ||||
\(681\) | 492.516 | 0.723224 | ||||||||
\(682\) | 10.8245 | + | 10.8245i | 0.0158717 | + | 0.0158717i | ||||
\(683\) | 18.6997 | − | 18.6997i | 0.0273787 | − | 0.0273787i | −0.693285 | − | 0.720664i | \(-0.743837\pi\) |
0.720664 | + | 0.693285i | \(0.243837\pi\) | |||||||
\(684\) | 213.399i | 0.311987i | ||||||||
\(685\) | −27.5006 | − | 44.0990i | −0.0401468 | − | 0.0643781i | ||||
\(686\) | −26.1916 | −0.0381802 | ||||||||
\(687\) | 619.741 | + | 619.741i | 0.902097 | + | 0.902097i | ||||
\(688\) | −217.933 | + | 217.933i | −0.316763 | + | 0.316763i | ||||
\(689\) | 234.192i | 0.339901i | ||||||||
\(690\) | 988.999 | − | 616.749i | 1.43333 | − | 0.893839i | ||||
\(691\) | −736.598 | −1.06599 | −0.532995 | − | 0.846119i | \(-0.678933\pi\) | ||||
−0.532995 | + | 0.846119i | \(0.678933\pi\) | |||||||
\(692\) | −204.174 | − | 204.174i | −0.295050 | − | 0.295050i | ||||
\(693\) | 195.533 | − | 195.533i | 0.282154 | − | 0.282154i | ||||
\(694\) | − | 275.251i | − | 0.396615i | ||||||
\(695\) | −60.8245 | + | 262.375i | −0.0875173 | + | 0.377517i | ||||
\(696\) | −230.049 | −0.330531 | ||||||||
\(697\) | −240.242 | − | 240.242i | −0.344680 | − | 0.344680i | ||||
\(698\) | 496.174 | − | 496.174i | 0.710852 | − | 0.710852i | ||||
\(699\) | 445.266i | 0.637004i | ||||||||
\(700\) | 125.158 | − | 42.8418i | 0.178797 | − | 0.0612025i | ||||
\(701\) | 518.483 | 0.739634 | 0.369817 | − | 0.929105i | \(-0.379420\pi\) | ||||
0.369817 | + | 0.929105i | \(0.379420\pi\) | |||||||
\(702\) | −57.5834 | − | 57.5834i | −0.0820277 | − | 0.0820277i | ||||
\(703\) | −530.766 | + | 530.766i | −0.755002 | + | 0.755002i | ||||
\(704\) | 111.733i | 0.158712i | ||||||||
\(705\) | −1790.68 | − | 415.121i | −2.53997 | − | 0.588823i | ||||
\(706\) | −184.325 | −0.261084 | ||||||||
\(707\) | 143.258 | + | 143.258i | 0.202628 | + | 0.202628i | ||||
\(708\) | −345.216 | + | 345.216i | −0.487594 | + | 0.487594i | ||||
\(709\) | − | 758.765i | − | 1.07019i | −0.844792 | − | 0.535095i | \(-0.820276\pi\) | ||
0.844792 | − | 0.535095i | \(-0.179724\pi\) | |||||||
\(710\) | 177.666 | + | 284.900i | 0.250234 | + | 0.401267i | ||||
\(711\) | −68.3487 | −0.0961304 | ||||||||
\(712\) | 160.000 | + | 160.000i | 0.224719 | + | 0.224719i | ||||
\(713\) | −22.2497 | + | 22.2497i | −0.0312058 | + | 0.0312058i | ||||
\(714\) | 173.925i | 0.243592i | ||||||||
\(715\) | −554.125 | + | 345.558i | −0.775000 | + | 0.483297i | ||||
\(716\) | −496.499 | −0.693435 | ||||||||
\(717\) | −87.4629 | − | 87.4629i | −0.121984 | − | 0.121984i | ||||
\(718\) | −592.232 | + | 592.232i | −0.824836 | + | 0.824836i | ||||
\(719\) | − | 16.7341i | − | 0.0232742i | −0.999932 | − | 0.0116371i | \(-0.996296\pi\) | ||
0.999932 | − | 0.0116371i | \(-0.00370429\pi\) | |||||||
\(720\) | −33.7998 | + | 145.800i | −0.0469441 | + | 0.202500i | ||||
\(721\) | −211.575 | −0.293446 | ||||||||
\(722\) | −157.700 | − | 157.700i | −0.218421 | − | 0.218421i | ||||
\(723\) | 115.791 | − | 115.791i | 0.160154 | − | 0.160154i | ||||
\(724\) | − | 34.3165i | − | 0.0473984i | ||||||
\(725\) | 220.367 | − | 449.748i | 0.303955 | − | 0.620342i | ||||
\(726\) | −425.266 | −0.585766 | ||||||||
\(727\) | 34.7836 | + | 34.7836i | 0.0478455 | + | 0.0478455i | 0.730625 | − | 0.682779i | \(-0.239229\pi\) |
−0.682779 | + | 0.730625i | \(0.739229\pi\) | |||||||
\(728\) | −49.4833 | + | 49.4833i | −0.0679716 | + | 0.0679716i | ||||
\(729\) | − | 466.083i | − | 0.639345i | ||||||
\(730\) | −334.949 | − | 77.6491i | −0.458835 | − | 0.106369i | ||||
\(731\) | 882.172 | 1.20680 | ||||||||
\(732\) | −499.333 | − | 499.333i | −0.682148 | − | 0.682148i | ||||
\(733\) | −754.703 | + | 754.703i | −1.02961 | + | 1.02961i | −0.0300602 | + | 0.999548i | \(0.509570\pi\) |
−0.999548 | + | 0.0300602i | \(0.990430\pi\) | |||||||
\(734\) | − | 84.1744i | − | 0.114679i | ||||||
\(735\) | 75.1916 | + | 120.575i | 0.102301 | + | 0.164047i | ||||
\(736\) | −229.666 | −0.312047 | ||||||||
\(737\) | 582.524 | + | 582.524i | 0.790399 | + | 0.790399i | ||||
\(738\) | 222.067 | − | 222.067i | 0.300903 | − | 0.300903i | ||||
\(739\) | − | 303.549i | − | 0.410756i | −0.978683 | − | 0.205378i | \(-0.934158\pi\) | ||
0.978683 | − | 0.205378i | \(-0.0658424\pi\) | |||||||
\(740\) | −446.700 | + | 278.566i | −0.603648 | + | 0.376441i | ||||
\(741\) | 541.341 | 0.730555 | ||||||||
\(742\) | −66.2583 | − | 66.2583i | −0.0892970 | − | 0.0892970i | ||||
\(743\) | 549.424 | − | 549.424i | 0.739467 | − | 0.739467i | −0.233008 | − | 0.972475i | \(-0.574857\pi\) |
0.972475 | + | 0.233008i | \(0.0748568\pi\) | |||||||
\(744\) | − | 8.89989i | − | 0.0119622i | ||||||
\(745\) | 95.5845 | − | 412.316i | 0.128301 | − | 0.553445i | ||||
\(746\) | 320.267 | 0.429312 | ||||||||
\(747\) | −590.932 | − | 590.932i | −0.791074 | − | 0.791074i | ||||
\(748\) | 226.142 | − | 226.142i | 0.302329 | − | 0.302329i | ||||
\(749\) | 102.459i | 0.136794i | ||||||||
\(750\) | −556.533 | − | 453.183i | −0.742044 | − | 0.604244i | ||||
\(751\) | 4.50056 | 0.00599275 | 0.00299638 | − | 0.999996i | \(-0.499046\pi\) | ||||
0.00299638 | + | 0.999996i | \(0.499046\pi\) | |||||||
\(752\) | 256.116 | + | 256.116i | 0.340580 | + | 0.340580i | ||||
\(753\) | −273.208 | + | 273.208i | −0.362826 | + | 0.362826i | ||||
\(754\) | 264.941i | 0.351380i | ||||||||
\(755\) | −106.346 | − | 24.6534i | −0.140855 | − | 0.0326535i | ||||
\(756\) | 32.5834 | 0.0430998 | ||||||||
\(757\) | −342.532 | − | 342.532i | −0.452486 | − | 0.452486i | 0.443693 | − | 0.896179i | \(-0.353668\pi\) |
−0.896179 | + | 0.443693i | \(0.853668\pi\) | |||||||
\(758\) | 749.066 | − | 749.066i | 0.988213 | − | 0.988213i | ||||
\(759\) | − | 2302.16i | − | 3.03315i | ||||||
\(760\) | 106.700 | + | 171.100i | 0.140394 | + | 0.225132i | ||||
\(761\) | −198.267 | −0.260535 | −0.130267 | − | 0.991479i | \(-0.541584\pi\) | ||||
−0.130267 | + | 0.991479i | \(0.541584\pi\) | |||||||
\(762\) | −369.141 | − | 369.141i | −0.484437 | − | 0.484437i | ||||
\(763\) | −289.729 | + | 289.729i | −0.379723 | + | 0.379723i | ||||
\(764\) | 401.832i | 0.525958i | ||||||||
\(765\) | 363.501 | − | 226.682i | 0.475164 | − | 0.296317i | ||||
\(766\) | 590.799 | 0.771278 | ||||||||
\(767\) | 397.575 | + | 397.575i | 0.518350 | + | 0.518350i | ||||
\(768\) | 45.9333 | − | 45.9333i | 0.0598089 | − | 0.0598089i | ||||
\(769\) | − | 423.158i | − | 0.550271i | −0.961405 | − | 0.275135i | \(-0.911277\pi\) | ||
0.961405 | − | 0.275135i | \(-0.0887227\pi\) | |||||||
\(770\) | 59.0086 | − | 254.541i | 0.0766346 | − | 0.330573i | ||||
\(771\) | 1553.50 | 2.01491 | ||||||||
\(772\) | 243.600 | + | 243.600i | 0.315543 | + | 0.315543i | ||||
\(773\) | 893.620 | − | 893.620i | 1.15604 | − | 1.15604i | 0.170722 | − | 0.985319i | \(-0.445390\pi\) |
0.985319 | − | 0.170722i | \(-0.0546101\pi\) | |||||||
\(774\) | 815.432i | 1.05353i | ||||||||
\(775\) | 17.3993 | + | 8.52531i | 0.0224508 | + | 0.0110004i | ||||
\(776\) | −226.183 | −0.291473 | ||||||||
\(777\) | −399.858 | − | 399.858i | −0.514618 | − | 0.514618i | ||||
\(778\) | 387.116 | − | 387.116i | 0.497579 | − | 0.497579i | ||||
\(779\) | − | 423.115i | − | 0.543152i | ||||||
\(780\) | 369.858 | + | 85.7417i | 0.474177 | + | 0.109925i | ||||
\(781\) | 663.182 | 0.849145 | ||||||||
\(782\) | 464.833 | + | 464.833i | 0.594416 | + | 0.594416i | ||||
\(783\) | 87.2282 | − | 87.2282i | 0.111403 | − | 0.111403i | ||||
\(784\) | − | 28.0000i | − | 0.0357143i | ||||||
\(785\) | 130.334 | + | 208.999i | 0.166030 | + | 0.266241i | ||||
\(786\) | −841.916 | −1.07114 | ||||||||
\(787\) | −820.137 | − | 820.137i | −1.04211 | − | 1.04211i | −0.999074 | − | 0.0430313i | \(-0.986298\pi\) |
−0.0430313 | − | 0.999074i | \(-0.513702\pi\) | |||||||
\(788\) | 430.250 | − | 430.250i | 0.546002 | − | 0.546002i | ||||
\(789\) | − | 1056.27i | − | 1.33875i | ||||||
\(790\) | −54.8009 | + | 34.1744i | −0.0693682 | + | 0.0432587i | ||||
\(791\) | −370.517 | −0.468416 | ||||||||
\(792\) | 209.033 | + | 209.033i | 0.263931 | + | 0.263931i | ||||
\(793\) | −575.066 | + | 575.066i | −0.725177 | + | 0.725177i | ||||
\(794\) | 564.407i | 0.710840i | ||||||||
\(795\) | −114.808 | + | 495.241i | −0.144413 | + | 0.622945i | ||||
\(796\) | 186.583 | 0.234401 | ||||||||
\(797\) | −300.653 | − | 300.653i | −0.377231 | − | 0.377231i | 0.492871 | − | 0.870102i | \(-0.335947\pi\) |
−0.870102 | + | 0.492871i | \(0.835947\pi\) | |||||||
\(798\) | −153.158 | + | 153.158i | −0.191928 | + | 0.191928i | ||||
\(799\) | − | 1036.73i | − | 1.29754i | ||||||
\(800\) | 45.7998 | + | 133.800i | 0.0572497 | + | 0.167250i | ||||
\(801\) | 598.665 | 0.747397 | ||||||||
\(802\) | 95.6502 | + | 95.6502i | 0.119265 | + | 0.119265i | ||||
\(803\) | −480.217 | + | 480.217i | −0.598029 | + | 0.598029i | ||||
\(804\) | − | 478.949i | − | 0.595708i | ||||||
\(805\) | 523.208 | + | 121.292i | 0.649947 | + | 0.150673i | ||||
\(806\) | −10.2497 | −0.0127168 | ||||||||
\(807\) | 64.5920 | + | 64.5920i | 0.0800397 | + | 0.0800397i | ||||
\(808\) | −153.150 | + | 153.150i | −0.189542 | + | 0.189542i | ||||
\(809\) | 1060.03i | 1.31030i | 0.755498 | + | 0.655150i | \(0.227395\pi\) | ||||
−0.755498 | + | 0.655150i | \(0.772605\pi\) | |||||||
\(810\) | −345.541 | − | 554.099i | −0.426594 | − | 0.684073i | ||||
\(811\) | 726.801 | 0.896179 | 0.448089 | − | 0.893989i | \(-0.352105\pi\) | ||||
0.448089 | + | 0.893989i | \(0.352105\pi\) | |||||||
\(812\) | −74.9580 | − | 74.9580i | −0.0923128 | − | 0.0923128i | ||||
\(813\) | −442.299 | + | 442.299i | −0.544033 | + | 0.544033i | ||||
\(814\) | 1039.81i | 1.27741i | ||||||||
\(815\) | −271.350 | + | 169.216i | −0.332945 | + | 0.207627i | ||||
\(816\) | −185.933 | −0.227859 | ||||||||
\(817\) | 776.842 | + | 776.842i | 0.950847 | + | 0.950847i | ||||
\(818\) | −113.875 | + | 113.875i | −0.139212 | + | 0.139212i | ||||
\(819\) | 185.150i | 0.226068i | ||||||||
\(820\) | 67.0161 | − | 289.083i | 0.0817270 | − | 0.352540i | ||||
\(821\) | 775.314 | 0.944354 | 0.472177 | − | 0.881504i | \(-0.343468\pi\) | ||||
0.472177 | + | 0.881504i | \(0.343468\pi\) | |||||||
\(822\) | 42.2002 | + | 42.2002i | 0.0513385 | + | 0.0513385i | ||||
\(823\) | 724.025 | − | 724.025i | 0.879738 | − | 0.879738i | −0.113769 | − | 0.993507i | \(-0.536292\pi\) |
0.993507 | + | 0.113769i | \(0.0362923\pi\) | |||||||
\(824\) | − | 226.183i | − | 0.274494i | ||||||
\(825\) | −1341.20 | + | 459.095i | −1.62570 | + | 0.556478i | ||||
\(826\) | −224.967 | −0.272357 | ||||||||
\(827\) | 301.457 | + | 301.457i | 0.364519 | + | 0.364519i | 0.865474 | − | 0.500954i | \(-0.167018\pi\) |
−0.500954 | + | 0.865474i | \(0.667018\pi\) | |||||||
\(828\) | −429.666 | + | 429.666i | −0.518921 | + | 0.518921i | ||||
\(829\) | 126.325i | 0.152382i | 0.997093 | + | 0.0761912i | \(0.0242760\pi\) | ||||
−0.997093 | + | 0.0761912i | \(0.975724\pi\) | |||||||
\(830\) | −769.266 | − | 178.334i | −0.926826 | − | 0.214860i | ||||
\(831\) | 1929.43 | 2.32182 | ||||||||
\(832\) | −52.8999 | − | 52.8999i | −0.0635816 | − | 0.0635816i | ||||
\(833\) | −56.6706 | + | 56.6706i | −0.0680319 | + | 0.0680319i | ||||
\(834\) | − | 309.283i | − | 0.370843i | ||||||
\(835\) | −291.990 | − | 468.226i | −0.349689 | − | 0.560750i | ||||
\(836\) | 398.282 | 0.476414 | ||||||||
\(837\) | 3.37458 | + | 3.37458i | 0.00403176 | + | 0.00403176i | ||||
\(838\) | −445.158 | + | 445.158i | −0.531215 | + | 0.531215i | ||||
\(839\) | − | 176.166i | − | 0.209971i | −0.994474 | − | 0.104986i | \(-0.966520\pi\) | ||
0.994474 | − | 0.104986i | \(-0.0334796\pi\) | |||||||
\(840\) | −128.900 | + | 80.3832i | −0.153452 | + | 0.0956943i | ||||
\(841\) | 439.664 | 0.522787 | ||||||||
\(842\) | −164.333 | − | 164.333i | −0.195169 | − | 0.195169i | ||||
\(843\) | 813.304 | − | 813.304i | 0.964773 | − | 0.964773i | ||||
\(844\) | − | 148.700i | − | 0.176184i | ||||||
\(845\) | −92.0840 | + | 397.216i | −0.108975 | + | 0.470079i | ||||
\(846\) | 958.299 | 1.13274 | ||||||||
\(847\) | −138.566 | − | 138.566i | −0.163596 | − | 0.163596i | ||||
\(848\) | 70.8331 | − | 70.8331i | 0.0835297 | − | 0.0835297i | ||||
\(849\) | 1109.98i | 1.30740i | ||||||||
\(850\) | 178.108 | − | 363.501i | 0.209538 | − | 0.427648i | ||||
\(851\) | −2137.33 | −2.51155 | ||||||||
\(852\) | −272.633 | − | 272.633i | −0.319992 | − | 0.319992i | ||||
\(853\) | −221.234 | + | 221.234i | −0.259359 | + | 0.259359i | −0.824793 | − | 0.565434i | \(-0.808709\pi\) |
0.565434 | + | 0.824793i | \(0.308709\pi\) | |||||||
\(854\) | − | 325.399i | − | 0.381030i | ||||||
\(855\) | 519.716 | + | 120.482i | 0.607855 | + | 0.140915i | ||||
\(856\) | −109.533 | −0.127959 | ||||||||
\(857\) | −777.533 | − | 777.533i | −0.907273 | − | 0.907273i | 0.0887786 | − | 0.996051i | \(-0.471704\pi\) |
−0.996051 | + | 0.0887786i | \(0.971704\pi\) | |||||||
\(858\) | 530.266 | − | 530.266i | 0.618025 | − | 0.618025i | ||||
\(859\) | − | 62.7987i | − | 0.0731067i | −0.999332 | − | 0.0365534i | \(-0.988362\pi\) | ||
0.999332 | − | 0.0365534i | \(-0.0116379\pi\) | |||||||
\(860\) | 407.716 | + | 653.800i | 0.474088 | + | 0.760232i | ||||
\(861\) | 318.758 | 0.370218 | ||||||||
\(862\) | −466.199 | − | 466.199i | −0.540834 | − | 0.540834i | ||||
\(863\) | −681.874 | + | 681.874i | −0.790121 | + | 0.790121i | −0.981513 | − | 0.191393i | \(-0.938700\pi\) |
0.191393 | + | 0.981513i | \(0.438700\pi\) | |||||||
\(864\) | 34.8331i | 0.0403161i | ||||||||
\(865\) | −612.523 | + | 381.975i | −0.708119 | + | 0.441590i | ||||
\(866\) | −442.549 | −0.511026 | ||||||||
\(867\) | −453.350 | − | 453.350i | −0.522895 | − | 0.522895i | ||||
\(868\) | 2.89989 | − | 2.89989i | 0.00334089 | − | 0.00334089i | ||||
\(869\) | 127.564i | 0.146794i | ||||||||
\(870\) | −129.883 | + | 560.266i | −0.149290 | + | 0.643984i | ||||
\(871\) | −551.591 | −0.633285 | ||||||||
\(872\) | −309.733 | − | 309.733i | −0.355198 | − | 0.355198i | ||||
\(873\) | −423.150 | + | 423.150i | −0.484707 | + | 0.484707i | ||||
\(874\) | 818.665i | 0.936688i | ||||||||
\(875\) | −33.6749 | − | 329.000i | −0.0384856 | − | 0.376000i | ||||
\(876\) | 394.833 | 0.450723 | ||||||||
\(877\) | −1019.15 | − | 1019.15i | −1.16208 | − | 1.16208i | −0.984018 | − | 0.178066i | \(-0.943016\pi\) |
−0.178066 | − | 0.984018i | \(-0.556984\pi\) | |||||||
\(878\) | 32.5662 | − | 32.5662i | 0.0370913 | − | 0.0370913i | ||||
\(879\) | 1988.98i | 2.26278i | ||||||||
\(880\) | 272.116 | + | 63.0829i | 0.309223 | + | 0.0716851i | ||||
\(881\) | −77.5673 | −0.0880446 | −0.0440223 | − | 0.999031i | \(-0.514017\pi\) | ||||
−0.0440223 | + | 0.999031i | \(0.514017\pi\) | |||||||
\(882\) | −52.3832 | − | 52.3832i | −0.0593914 | − | 0.0593914i | ||||
\(883\) | 954.566 | − | 954.566i | 1.08105 | − | 1.08105i | 0.0846371 | − | 0.996412i | \(-0.473027\pi\) |
0.996412 | − | 0.0846371i | \(-0.0269731\pi\) | |||||||
\(884\) | 214.133i | 0.242232i | ||||||||
\(885\) | 645.841 | + | 1035.65i | 0.729763 | + | 1.17022i | ||||
\(886\) | −625.699 | −0.706206 | ||||||||
\(887\) | 307.150 | + | 307.150i | 0.346279 | + | 0.346279i | 0.858722 | − | 0.512442i | \(-0.171259\pi\) |
−0.512442 | + | 0.858722i | \(0.671259\pi\) | |||||||
\(888\) | 427.466 | − | 427.466i | 0.481381 | − | 0.481381i | ||||
\(889\) | − | 240.558i | − | 0.270593i | ||||||
\(890\) | 480.000 | − | 299.333i | 0.539326 | − | 0.336329i | ||||
\(891\) | −1289.82 | −1.44760 | ||||||||
\(892\) | −225.858 | − | 225.858i | −0.253204 | − | 0.253204i | ||||
\(893\) | 912.948 | − | 912.948i | 1.02234 | − | 1.02234i | ||||
\(894\) | 486.032i | 0.543660i | ||||||||
\(895\) | −280.316 | + | 1209.18i | −0.313203 | + | 1.35104i | ||||
\(896\) | 29.9333 | 0.0334077 | ||||||||
\(897\) | 1089.96 | + | 1089.96i | 1.21511 | + | 1.21511i | ||||
\(898\) | 276.582 | − | 276.582i | 0.307998 | − | 0.307998i | ||||
\(899\) | − | 15.5264i | − | 0.0172708i | ||||||
\(900\) | 336.000 | + | 164.633i | 0.373333 | + | 0.182925i | ||||
\(901\) | −286.726 | −0.318230 | ||||||||
\(902\) | −414.459 | − | 414.459i | −0.459488 | − | 0.459488i | ||||
\(903\) | −585.241 | + | 585.241i | −0.648108 | + | 0.648108i | ||||
\(904\) | − | 396.099i | − | 0.438163i | ||||||
\(905\) | −83.5748 | − | 19.3746i | −0.0923479 | − | 0.0214084i | ||||
\(906\) | 125.358 | 0.138365 | ||||||||
\(907\) | −608.192 | − | 608.192i | −0.670553 | − | 0.670553i | 0.287290 | − | 0.957844i | \(-0.407246\pi\) |
−0.957844 | + | 0.287290i | \(0.907246\pi\) | |||||||
\(908\) | −171.559 | + | 171.559i | −0.188941 | + | 0.188941i | ||||
\(909\) | 573.033i | 0.630400i | ||||||||
\(910\) | 92.5748 | + | 148.450i | 0.101731 | + | 0.163132i | ||||
\(911\) | 1336.46 | 1.46703 | 0.733515 | − | 0.679673i | \(-0.237878\pi\) | ||||
0.733515 | + | 0.679673i | \(0.237878\pi\) | |||||||
\(912\) | −163.733 | − | 163.733i | −0.179532 | − | 0.179532i | ||||
\(913\) | −1102.90 | + | 1102.90i | −1.20799 | + | 1.20799i | ||||
\(914\) | − | 154.883i | − | 0.169456i | ||||||
\(915\) | −1498.00 | + | 934.166i | −1.63716 | + | 1.02095i | ||||
\(916\) | −431.750 | −0.471343 | ||||||||
\(917\) | −274.325 | − | 274.325i | −0.299155 | − | 0.299155i | ||||
\(918\) | 70.5006 | − | 70.5006i | 0.0767980 | − | 0.0767980i | ||||
\(919\) | − | 358.632i | − | 0.390241i | −0.980779 | − | 0.195121i | \(-0.937490\pi\) | ||
0.980779 | − | 0.195121i | \(-0.0625099\pi\) | |||||||
\(920\) | −129.666 | + | 559.333i | −0.140942 | + | 0.607970i | ||||
\(921\) | 1409.65 | 1.53056 | ||||||||
\(922\) | 615.600 | + | 615.600i | 0.667678 | + | 0.667678i | ||||
\(923\) | −313.983 | + | 313.983i | −0.340176 | + | 0.340176i | ||||
\(924\) | 300.049i | 0.324729i | ||||||||
\(925\) | 426.224 | + | 1245.17i | 0.460783 | + | 1.34613i | ||||
\(926\) | −293.132 | −0.316558 | ||||||||
\(927\) | −423.150 | − | 423.150i | −0.456472 | − | 0.456472i | ||||
\(928\) | 80.1335 | − | 80.1335i | 0.0863507 | − | 0.0863507i | ||||
\(929\) | 399.023i | 0.429518i | 0.976667 | + | 0.214759i | \(0.0688967\pi\) | ||||
−0.976667 | + | 0.214759i | \(0.931103\pi\) | |||||||
\(930\) | −21.6749 | − | 5.02475i | −0.0233064 | − | 0.00540296i | ||||
\(931\) | −99.8084 | −0.107206 | ||||||||
\(932\) | −155.100 | − | 155.100i | −0.166416 | − | 0.166416i | ||||
\(933\) | 933.282 | − | 933.282i | 1.00030 | − | 1.00030i | ||||
\(934\) | 190.142i | 0.203578i | ||||||||
\(935\) | −423.073 | − | 678.426i | −0.452485 | − | 0.725590i | ||||
\(936\) | −197.933 | −0.211467 | ||||||||
\(937\) | 149.237 | + | 149.237i | 0.159271 | + | 0.159271i | 0.782244 | − | 0.622973i | \(-0.214075\pi\) |
−0.622973 | + | 0.782244i | \(0.714075\pi\) | |||||||
\(938\) | 156.058 | − | 156.058i | 0.166373 | − | 0.166373i | ||||
\(939\) | − | 1309.17i | − | 1.39421i | ||||||
\(940\) | 768.349 | − | 479.150i | 0.817392 | − | 0.509734i | ||||
\(941\) | −719.397 | −0.764503 | −0.382251 | − | 0.924058i | \(-0.624851\pi\) | ||||
−0.382251 | + | 0.924058i | \(0.624851\pi\) | |||||||
\(942\) | −200.000 | − | 200.000i | −0.212314 | − | 0.212314i | ||||
\(943\) | 851.916 | − | 851.916i | 0.903410 | − | 0.903410i | ||||
\(944\) | − | 240.499i | − | 0.254766i | ||||||
\(945\) | 18.3961 | − | 79.3541i | 0.0194668 | − | 0.0839726i | ||||
\(946\) | 1521.90 | 1.60877 | ||||||||
\(947\) | −35.9408 | − | 35.9408i | −0.0379522 | − | 0.0379522i | 0.687876 | − | 0.725828i | \(-0.258543\pi\) |
−0.725828 | + | 0.687876i | \(0.758543\pi\) | |||||||
\(948\) | 52.4413 | − | 52.4413i | 0.0553179 | − | 0.0553179i | ||||
\(949\) | − | 454.717i | − | 0.479154i | ||||||
\(950\) | 476.941 | − | 163.257i | 0.502043 | − | 0.171850i | ||||
\(951\) | −1807.47 | −1.90060 | ||||||||
\(952\) | −60.5834 | − | 60.5834i | −0.0636381 | − | 0.0636381i | ||||
\(953\) | 178.057 | − | 178.057i | 0.186838 | − | 0.186838i | −0.607489 | − | 0.794328i | \(-0.707823\pi\) |
0.794328 | + | 0.607489i | \(0.207823\pi\) | |||||||
\(954\) | − | 265.033i | − | 0.277813i | ||||||
\(955\) | 978.628 | + | 226.869i | 1.02474 | + | 0.237559i | ||||
\(956\) | 60.9321 | 0.0637366 | ||||||||
\(957\) | 803.254 | + | 803.254i | 0.839346 | + | 0.839346i | ||||
\(958\) | 32.0667 | − | 32.0667i | 0.0334726 | − | 0.0334726i | ||||
\(959\) | 27.5006i | 0.0286763i | ||||||||
\(960\) | −85.9333 | − | 137.800i | −0.0895138 | − | 0.143541i | ||||
\(961\) | −960.399 | −0.999375 | ||||||||
\(962\) | −492.299 | − | 492.299i | −0.511746 | − | 0.511746i | ||||
\(963\) | −204.917 | + | 204.917i | −0.212790 | + | 0.212790i | ||||
\(964\) | 80.6674i | 0.0836799i | ||||||||
\(965\) | 730.799 | − | 455.733i | 0.757304 | − | 0.472262i | ||||
\(966\) | −616.749 | −0.638457 | ||||||||
\(967\) | −288.417 | − | 288.417i | −0.298259 | − | 0.298259i | 0.542073 | − | 0.840332i | \(-0.317640\pi\) |
−0.840332 | + | 0.542073i | \(0.817640\pi\) | |||||||
\(968\) | 148.133 | − | 148.133i | 0.153030 | − | 0.153030i | ||||
\(969\) | 662.775i | 0.683978i | ||||||||
\(970\) | −127.700 | + | 550.849i | −0.131649 | + | 0.567886i | ||||
\(971\) | −212.474 | −0.218819 | −0.109410 | − | 0.993997i | \(-0.534896\pi\) | ||||
−0.109410 | + | 0.993997i | \(0.534896\pi\) | |||||||
\(972\) | 451.867 | + | 451.867i | 0.464883 | + | 0.464883i | ||||
\(973\) | 100.775 | − | 100.775i | 0.103571 | − | 0.103571i | ||||
\(974\) | 898.648i | 0.922636i | ||||||||
\(975\) | 417.633 | − | 852.349i | 0.428341 | − | 0.874204i | ||||
\(976\) | 347.867 | 0.356421 | ||||||||
\(977\) | 53.5662 | + | 53.5662i | 0.0548272 | + | 0.0548272i | 0.733989 | − | 0.679162i | \(-0.237656\pi\) |
−0.679162 | + | 0.733989i | \(0.737656\pi\) | |||||||
\(978\) | 259.666 | − | 259.666i | 0.265507 | − | 0.265507i | ||||
\(979\) | − | 1117.33i | − | 1.14130i | ||||||
\(980\) | −68.1916 | − | 15.8084i | −0.0695833 | − | 0.0161310i | ||||
\(981\) | −1158.91 | −1.18136 | ||||||||
\(982\) | −322.216 | − | 322.216i | −0.328123 | − | 0.328123i | ||||
\(983\) | 612.070 | − | 612.070i | 0.622655 | − | 0.622655i | −0.323554 | − | 0.946210i | \(-0.604878\pi\) |
0.946210 | + | 0.323554i | \(0.104878\pi\) | |||||||
\(984\) | 340.766i | 0.346307i | ||||||||
\(985\) | −804.924 | − | 1290.75i | −0.817181 | − | 1.31041i | ||||
\(986\) | −324.372 | −0.328978 | ||||||||
\(987\) | 687.778 | + | 687.778i | 0.696837 | + | 0.696837i | ||||
\(988\) | −188.566 | + | 188.566i | −0.190856 | + | 0.190856i | ||||
\(989\) | 3128.25i | 3.16304i | ||||||||
\(990\) | 627.100 | − | 391.066i | 0.633434 | − | 0.395016i | ||||
\(991\) | −699.666 | −0.706020 | −0.353010 | − | 0.935619i | \(-0.614842\pi\) | ||||
−0.353010 | + | 0.935619i | \(0.614842\pi\) | |||||||
\(992\) | 3.10011 | + | 3.10011i | 0.00312511 | + | 0.00312511i | ||||
\(993\) | −187.417 | + | 187.417i | −0.188738 | + | 0.188738i | ||||
\(994\) | − | 177.666i | − | 0.178739i | ||||||
\(995\) | 105.342 | − | 454.408i | 0.105872 | − | 0.456691i | ||||
\(996\) | 906.799 | 0.910440 | ||||||||
\(997\) | 682.529 | + | 682.529i | 0.684582 | + | 0.684582i | 0.961029 | − | 0.276447i | \(-0.0891570\pi\) |
−0.276447 | + | 0.961029i | \(0.589157\pi\) | |||||||
\(998\) | 925.648 | − | 925.648i | 0.927503 | − | 0.927503i | ||||
\(999\) | 324.166i | 0.324490i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 70.3.f.a.57.2 | yes | 4 | |
3.2 | odd | 2 | 630.3.o.a.127.1 | 4 | |||
4.3 | odd | 2 | 560.3.bh.b.337.1 | 4 | |||
5.2 | odd | 4 | 350.3.f.b.43.1 | 4 | |||
5.3 | odd | 4 | inner | 70.3.f.a.43.2 | ✓ | 4 | |
5.4 | even | 2 | 350.3.f.b.57.1 | 4 | |||
7.6 | odd | 2 | 490.3.f.d.197.1 | 4 | |||
15.8 | even | 4 | 630.3.o.a.253.1 | 4 | |||
20.3 | even | 4 | 560.3.bh.b.113.1 | 4 | |||
35.13 | even | 4 | 490.3.f.d.393.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.3.f.a.43.2 | ✓ | 4 | 5.3 | odd | 4 | inner | |
70.3.f.a.57.2 | yes | 4 | 1.1 | even | 1 | trivial | |
350.3.f.b.43.1 | 4 | 5.2 | odd | 4 | |||
350.3.f.b.57.1 | 4 | 5.4 | even | 2 | |||
490.3.f.d.197.1 | 4 | 7.6 | odd | 2 | |||
490.3.f.d.393.1 | 4 | 35.13 | even | 4 | |||
560.3.bh.b.113.1 | 4 | 20.3 | even | 4 | |||
560.3.bh.b.337.1 | 4 | 4.3 | odd | 2 | |||
630.3.o.a.127.1 | 4 | 3.2 | odd | 2 | |||
630.3.o.a.253.1 | 4 | 15.8 | even | 4 |